Stir together cookie crumbs and butter; press firmly into bottom of a 10" springform pan.
Bake at 325° for 12 minutes. Cool on a wire rack.
Meanwhile, beat cream cheese at medium speed with an electric mixer until creamy; gradually add sugar, beating well. Add eggs, 1 at a time, beating until blended after each addition. Stir coffee, liqueur, and vanilla into batter.
Reserve 2 1/2 cups batter; pour remaining batter into crust.
Stir melted chocolate into reserved batter. Spoon dollops of chocolate batter over coffee batter. Swirl batter gently with a knife.
Place springform pan in a large round shallow pan, and add hot water to shallow pan to a depth of 2".
Bake at 325° for 55 minutes or until cheesecake is almost set. Turn off oven, and let cheesecake stand in closed oven 30 minutes. Remove from oven; gently run a knife around edges to loosen sides. Cool on a wire rack; cover and chill 8 hours.