Mix together the graham cracker crumbs, melted butter, and 2 Tbsp. of sugar until well combined. Press into the bottom of a 9-in. springform pan that has been sprayed with cooking spray. Press 1 inch up the sides. Bake in a preheated 350-degree oven for 8 minutes, then remove to cool on a wire rack.
Reduce oven temperature to 325 degrees F.
Beat the softened cream cheese in a large bowl with an electric mixer until fluffy. Gradually add 1 cup of sugar, beating until blended. Add eggs one at a time, beating well after each addition. Stir in sour cream, espresso and vanilla. Pour batter into the baked and cooled crust.
Bake cheesecake in the preheated oven for 1 hour and 5 minutes; then turn the oven off, partially open the door and allow the cheesecake to rest for 15 minutes more. Remove from the oven, and run a knife around the edges. Cool cheesecake on a wire rack to room temperature, then cover the springform pan with plastic wrap, and chill in the refrigerator for 8 hours.
To serve, cut the cheesecake into wedges and garnish each slice with whipped cream and caramel sauce.