1. Preheat the oven to 350°F. Generously butter the bottom and sides of a 9-inch springform pan. Wrap the outside with aluminum foil, covering the bottom and extending all the way up the sides. Make and bake the cake crust and leave it in the pan. Keep the oven on.

2. Dissolve the instant espresso in the hot water in a small cup and let stand. Put one package of the cream cheese, 1/3 cup of the sugar, and the cornstarch in a large bowl. Beat with an electric mixer on low until creamy, about 3 minutes, scraping the bowl down several times. Blend in the remaining cream cheese, one package at a time, scraping down the bowl after each one. Increase the mixer speed to medium and beat in the remaining 1 1/3 cups sugar, then the vanilla. Blend in the eggs, one at a time, beating well after adding each one. Stir the dissolved coffee into the cream, then beat into the cream cheese mixture just until completely blended. Be carefrul not to overmix! Gently spoon the batter on top of the cake crust.

3. Place the cake in a large shallow pan containing hot water that comes about 1 inch up the sides of the springform. Bake until the edges are light golden brown and the top is light tan, about 1¼ hours. Remove the cheesecake from the water bath, transfer to a wire rack, and let the cake cool for 2 hours (just walk away-don’t move it). Leave the cake in the pan, cover loosely with plastic wrap, and refrigerate until completely cold, preferably overnight or at least 4 hours.

4. To decorate, release and remove the sides of the springform, leaving the cake on the bottom of the pan. Place on a cake plate. Cover the top with the chocolate curls and dust with the cocoa. Decorate the center of the cake with a few coffee beans if you wish (be sure to remove them before serving). Refrigerate until ready to serve. Slice the cold cake with a sharp straight-edge knife, not a serrated one. Cover any leftover cake and refrigerate, or wrap and freeze for up to 1 month.