Grease a 13x9x2-inch baking pan; set aside. Preheat oven to 350 degrees F.

For crust: In a medium bowl, stir together 1 egg and 1/2 cup melted butter. Stir in dry cake mix until combined (may need to work together by hand; mixture will be thick). Press evenly into the bottom of prepared pan. Bake 15 minutes.

Meanwhile, for topping: In a large bowl, beat cream cheese with an electric mixer until fluffy. Add 2 eggs, one at a time, beating on low speed after each addition just until combined. Gradually add 16 ounces powdered sugar, 1 cup at a time, beating on low speed until smooth. Slowly add 1/2 cup melted butter, chocolate topping, coffee and vanilla, continuing to beat on low speed until just combined. Pour batter over baked cake crust.

Bake for 35 minutes more (center will not appear to be set). Cool completely in pan on a wire rack before serving. If you like, sprinkle with additional powdered sugar. Cut into bars. Makes 24 bars.