Preheat oven to 350°.
Combine 3/4 cup sugar and butter in a bowl; beat at medium speed of a mixer for 3 minutes. Add milk and liqueur; beat well. Lightly spoon flour into a dry measuring cup; level with a knife. Combine flour, 1/4 cup cocoa, baking powder, and salt in a bowl; gradually add to sugar mixture, beating until well-blended. Spoon batter into an 8-inch square baking pan coated with cooking spray.
Combine 1/4 cup cocoa, 2/3 cup sugar, and coffee granules in a small bowl; sprinkle over batter. Pour boiling water over batter (do not stir). Bake at 350° for 30 minutes or until cake springs back when touched lightly in the center (cake will not test clean when a wooden pick is inserted in center). Serve warm with ice cream.