Curated this - because there was some confusion as to the proportions of this drink, I asked Julie Reiner and she sent me a picture of the recipe (which must be from The Craft Cocktail Party). Updated this to the specified brands - she's specific about them, changed 1 dash of Angostura to 2. Thanks,  Zachary

Should this be called "The Slope" rather than just "Slope"? That is the primary way I see it listed, and it refers to a neighborhood, so the emphasis would make sense here. There seem to be a LOT of slight variations of this cocktail including later versions (plural) attributed to Julie Reiner herself. There is a 2017 video by her using Maker's Mark bourbon (rather than rye) and Giffard Apricot--so it doesn't look like formula is set as one might expect. In various recipes on the web the base spirit is listed from 2 to 2 1/4 to 2 1/2 oz, while apricot is from 1/4 to 1/2 and Angostura bitters from 1 to 2 dashes.

I tried two different versions of this tonight based on a slightly different recipe and thought it was quite good (as did the others who sampled what I made.) I used "only" 2 oz of Rittenhouse Rye for both, with 3/4 Punt e Mes, and 1/4 R&W Apricot. This had plenty of peppery rye and alcohol heat which reinforced the bitter components in Punt e Mes. I used a single dash of Angostura for one, and a single dash of Abbott's bitters (my own bottling based on Darcy O'Neil's recipe) for the other.

The Angostura was pretty noticeable at only a dash, and this cocktail is a good candidate for experimenting with different aromatic bitters to appreciate the differences they provide. I somewhat preferred the cardamom/clove/fennel from the Abbott's over the more cinnamon baking spice of the Angostura, but others were evenly split as to preference.

I used J pear liqueur (60 proof) and not true eau de vie. Quite tasty, indeed; the maraschino didn't have a chance to dominate. Powerful sweet. The only real drawback I can see is the risk of diabetes. 4/5.

Yes, I would not substitute Pear Liqueur without re-designing the drink. It would be way too sweet for the amount of acid, and would overpower the other flavors, since Pear Eau-de-vie was a much more subtle flavor.

Not bad but the maraschino dominated some for us and as such the ginger and lemon juice were a little lost. Would probably tweak the ratios a bit. Beautiful color. 

Used closer to 1/4 Maraschino (Luxardo), with Pear Williams Purkhart Eau-de-Vie, and Canton for the ginger. the look is a bit like pink lemonade; the flavor is soft floral and fruity. I think a few extra dashes of Peychaud's only help make this drink better.

Maybe they're going for the citrus + spice thing?

Recipe updated based upon response from creator. Name and recipe changed.

basically a Gilroy with slightly different ratios?

Can't see this is in the Old Waldorf Astoria bar book.

The name "Tipperary Cocktail" is from Old Waldorf Astoria, but the proper credit for this particular version is Gaz Regan, who wrote the SF Gate article that is the referenced. From that article:

The earliest recipe I can find is in "The Old Waldorf-Astoria Bar Book," where author Albert Stevens Crockett declares that the drink predates the popular World War I song, "It's a Long Way to Tipperary." That particular ditty was penned in 1912, so we can probably surmise that the drink was created in the first decade of the 20th century. The formula, though, is pretty vile. I doubt that even a Yorkshire dweller - let alone a sturdy man from Tipperary - would put himself behind a glass full of sloe gin and dry vermouth with a little lemon juice.

Curated to clarify history and creator. Thanks @noksagt

Curated (can you curate yourself?) to remove my demented substitution of Meletti for Amer Picon. They are nothing alike. If you want to substitute, use Amaro CioCiaro or Amaro Lucano for the Amer Picon. Absent that, use Amaro Ramazzotti and a dash or two of Angostura Orange bitters. I would like to say I loved this drink given its great history and NYC borough name. I can't. With less Maraschino and more Amer Picon, I might enjoy it. It would also benefit from a bitter bone-dry vermouth, like Sutton Cellars Brown label.

I merged in another Brooklyn recipe posted by Zachary, keeping this one from Ted Haigh's book. The two recipes were very similar. The newly-available Bittermen's Amere Nouvelle makes a good substitution for Amer Picon, although it is quite light in flavor.

Is this really supposed to be equal amounts of rye and dry vermouth? I like this drink with more of a 3:1 ratio

The Staub recipe is 1/2 jigger French vermouth and 1/2 jigger "good rye whisky" - it's a small, weird drink.

Hmm, interesting. I make this (apparently historically inaccurate, but to my mind preferable) version: http://www.seriouseats.com/recipes/2011/02/the-brooklyn-cocktail-rye-ma…. I guess it is 2:1, not 3:1.

We have this on our menu right now and we steer away from original ratios and go with 2 oz rye, 3/4 oz dry vermouth, tsp maraschino and a tsp amer picon. More of a current "Manhattan" ratio.

Used the Serious Eats 2:1 ratio with Alberta Premium rye and Cocchi Americano, and 1/4 oz. Luxardo. Couple of dashes of Angostura, few drops of Scrappy's orange & cardamom and a few drops of Regan's. Very tasty! Great balance and good strength. Love the rye spiciness!

That sounds good, but without dry vermouth and Amer Picon (or sub) would be a rather different drink. I recently had a Brooklyn at B Street in Newtow, MA and it reminded me what a nice drink this is. When a bar has "Housemade Amer Picon", it's hard to resist ordering something with it. (They use Boudreau's recipe.)

If you haven't had a Redhook, I recommend it (Rye, Punt e Mes, Maraschino). You could try Cocchi in here too.

I was an idiot, but no longer. This is a fantastic drink. I use Bigallet 'China-China' Amer for the Amer Picon. Also wonderful is the substitution of 1/4 oz Islay Scotch (e.g. Laphroaig 10) for a bit of the rye. This is a world-class cocktail.

Great cocktail, though I definitely prefer the original (Jack's Manual, 1908) version with Sweet Vermouth.

Note: the drink was first published as Green Chartreuse but it is far superior with Yellow to my palate, so that's how I (and most folks) make it.