Shake with ice and strain into a pre-cooled cocktail glass.
The original receipe was made with White Crème de Cacao, but Brown works also quite well.
Garnishing with grated nutmeg was not part of the original receipe (which resulted in a plain white cocktail), but is common today.
There are many variants in terms of the ratio of the ingredients. Most common is an increased amount of gin.
The Alexander is the ancester of many of todays famous cocktails, like the Brandy Alexander, the Grasshopper, the Golden Dream or the White Russian. The receipe was first mentioned in Hugo Ensslin's Recipes for Mixed Drinks in 1916.
One legend says that the Alexander was created to celebrate the advertising character of Phoebe Snow, who was dressed completely in white.
Recipes for Mixed Drinks, Hugo R. Ensslin, 1916,
http://www.classicmixology.com/cocktails/alexander_cocktail/1916