Preheat oven to 375°F.
Combine flour, 1 Tablespoon ground coffee beans, cocoa, and sugar. Cut in butter until mixture resembles coarse crumbs. Add egg and mix until evenly moistened. (Mixture will appear rather dry.)
Spread mixture evenly in a 10-inch springform pan with 3 inch sides; then press firmly over the bottom of the pan and half way up the sides. Bake 8 minutes. Set aside.
Preheat oven to 450°F.
In a large bowl combine cream cheese, sugar, 2 tablespoons flour and 1½ tablespoon ground coffee beans; beat until well blended. Add eggs one at a time, mixing well after each addition. Blend in sour cream, Irish cream liqueur, and brewed espresso coffee. Pour filling into prepared crust. Bake at 450°F for 10 minutes.
Reduce oven temperature to 250°F and continue baking for 50 to 55 minutes or until top is browned, edges have puffed; and the center is still slightly moist and jiggles when the pan is tapped. With a knife loosen cake from rim of pan. Cool completely before unmolding. Cover and refrigerate at least six hour before serving. If desired, garnish top with chocolate curls or chocolate espresso beans.