Fill a cocktail glass with ice and place in the freezer to chill.
Meanwhile, add 2 ounces of Rye Whiskey, 1½ ounces of Sweet Vermouth, and 3 dashes of bitters to a mixing glass filled with ice.
Stir the mixture until well chilled.
Remove the chilled cocktail glass from the freezer and discard the ice.
Rinse the chilled glass with a few teaspoons of absinthe.
Strain the ingredients from the mixing glass into the prepared cocktail glass.