Ti Adelaide Martin and Lally Brennan's Sazerac

Pour Absinthe into a rocks glass; swirl to coat. Pour out any excess Absinthe; fill glass with ice to chill.

Place rye, simple syrup, and bitters in a cocktail shaker; fill with ice. Cover and shake vigorously.

Discard ice from rocks glass and strain rye mixture into glass. Rub rim of glass with lemon twist and add to cocktail; serve immediately.