For Crust: Position rack in center of oven and preheat to 400 degrees F.
Grind the cookies in a food processor. Add butter and pulse until crumbs are moistened.
Press the crumbs on the bottom and 1 1/2 inches up the sides of a 9-inch springform pan. Wrap the outside of the pan with aluminum foil.
For Filling: In a small bowl, dissolve the espresso powder in 1 TB water. Using an electric mixer, beat cream cheese in a large bowl until smooth.Add sugar and continue to beat until mixture is light and fluffy. Add eggs 1 at a time, beating well after each addition. Mix in the espresso mixture, butter and coffe.
Combine chocolate and cream in a heavy small saucepan. Stir over low heat until chocolate melts. pour half of the cheese filling (about 2 1/2 cups) into prepared crust. Drop 5 TB melted chocolate mixture by TBsful aroun the edge of filling. spacing evenly. use a small sharp knife to swirl chocolate into the filling. Carefully pour the remaining cheese filling over the swirled mixture. Drop remaining chocolate mxture by TBsful into center 6 inches of filling, spacing evenly. Swirl mixture together using tip of knife.
Bake cheesecake until edges are puffed and beginning to crack and top is golden brown, about 40 minutes. The center will not be set. Cool on a rack. Cover and chill overnight in the refrigerator.
Next day, run a small sharp knife around the edge of the pan to loosen the cheesecake. Release the sides from the pan. Let cheesecake stand at room temperature for 30 minutes before serving.
Transfer to a platter and serve.