Preheat oven to 325°.
Combine 1/3 cup sugar and 3 tablespoons water in a small, heavy saucepan over medium-high heat; cook until sugar dissolves, stirring frequently. Continue cooking until golden (about 4 minutes). Immediately pour into 4 (6-ounce) ramekins or custard cups coated with cooking spray, tilting each cup quickly until caramelized sugar coats bottom of cup. Set aside.
Beat eggs and egg white in a medium bowl with a whisk. Stir in 1/2 cup sugar, liqueur, espresso, salt, and milk. Divide mixture evenly among prepared custard cups. Place cups in a 9-inch square baking pan; add hot water to pan to a depth of 1 inch. Bake at 325° for 55 minutes or until a knife inserted in center comes out clean. Remove cups from pan. Cover and chill at least 4 hours.
Loosen edges of custards with a knife or rubber spatula. Place a dessert plate, upside down, on top of each cup; invert onto plates. Drizzle any remaining caramelized syrup over custards. Garnish with chopped coffee beans, if desired.