For the Cardamom Tincture:
Combine the cardamom pods and vodka and let sit for 48 hours. Strain and reserve the liquid only.
To Assemble and Serve:
Put the whiskey, lemon juice, gomme, and egg whites in a cocktail shaker with ice. Shake vigorously, then pour through a fine strainer into a chilled coupe. Top with the bitters and 3 dashes of cardamom tincture.