It's called a Sazerac.
It's the oldest cocktail in America, and is made with Rye whiskey (1.5oz- original recipe calls for cognac), 1-2 sugar cubes or simple syrup, peychauds (3-4 dashes) and angostura bitters (2 dashes), an absynthe rinse, and a lemon peel squeezed and thrown in. Served neat. Delicious.
You also use two glasses when you prepare it. One with ice water while you make everything in the other with ice in it, then you dump the ice water glass that is now chilled, rinse with absynthe, and dump the contents sans ice in the glass. Twist the lemon peel, toss it in, and enjoy the licorice/rye goodness.