Preheat oven to 325°F. Line the bottom of a 9-inch spring-form pan with parchment and butter the sides of the pan.
In a small bowl blend together sugar, corn starch, cocoa powder and ground coffee beans. Set aside.
In a large bowl beat cream at low speed until smooth. Add sugar mixture and continue to mix at low speed until and beat until well blended.
Add eggs one at a time, mixing well after each addition. Blend coffee liqueur.
Pour filling into prepared pan. Bake 40 to 45 minutes or until top is just barely set. (The center is still slightly moist and jiggles when the pan is tapped.) Turn off oven and leave cheese cake in the oven for additional 15 minutes.
Remove pan from oven and let cool on a rack. While the cake is still warm run a thin knife around the edge but do not remove the pan rim. Let cool completely at room temperature for about 1½ hours.
Cover and refrigerate. When thoroughly chilled (at least 6 hours) the cheesecake may be removed from the pan and parchment removed. Use a knife point to release the edges of the cake from the pan bottom and slide a cake lifter or very large turner under the parchment and cake moved to a serving platter. The parchment can be carefully peeled off during the transfer or left on.
Use a vegetable peeler to shave chocolate curls over the top of the cake or combine chocolate curls and chocolate coated espresso beans for garnish.
This recipe is gluten-free.