Fill a cocktail shaker halfway full with ice. Add the rye whiskey, Benedictine and bitters. Shake well for at least 30 seconds, then strain into a cocktail (martini) glass. Garnish with a cherry.
This is a variation on the Manhattan, with Benedictine standing in for vermouth and Peychaud's bitters for Angostura bitters. Rye whiskey is significantly different from bourbon; it's spicier and funkier, and it mingles well with different liqueurs and bitters.
Be sure to use a higher-proof rye, such as Rittenhouse Rye (100 proof) or Wild Turkey 101.