Place the sugar cube and a few drops of water in a heavy mixing glass and crush the sugar cube until it dissolves. Add Peychaud’s bitters, Angostura bitters, rye whiskey, a few pieces of ice, and stir. Coat the interior of a chilled heavy-bottomed glass with absinthe, drain off the excess. Strain the contents from the mixing glass into the chilled, absinthe-coated glass. Twist the lemon peel over the top.