Coffee Mixture for ladyfingers:
Combine the 1/2 cup water and 1 tablespoon espresso in a small saucepan until dissolved. Add 2 tablespoons sugar and 2 tablespoons coffee liqueur. Bring to a boil, reduce heat to medium and let simmer for 3 minutes, uncovered, stirring a few times.
Stir 1 tablespoon hot water and 1 tablespoon instant coffee together in a small cup until dissolved. Let cool. Stir coffee mixture into 2/3 cup heavy cream. Set aside. Preheat oven to 350 degrees Fahrenheit. Generously butter the bottom and sides of an 8 or 9-inch springform pan (oddly, mine is 8 1/2-inch). Dip 12 ladyfinger cookies into the coffee mixture just long enough to get them wet, do not soak them! Arrange the ladyfingers on the bottom of the pan. (break or cut the last one to fit and fill the gaps). Wrap the outside of the pan with aluminum foil, covering the bottom and extending up the sides.
In a large bowl, with an electric mixer, beat one package of the cream cheese, 1/3 cup of the sugar, and 1/4 cup cornstarch on low speed until smooth. Scrape the sides of the bowl and beaters with a spatula as needed. Blend in remaining 2 packages of the cheese, one package at a time. Add the 2 eggs, one at a time, and continue to beat slowly until combined. Beat in the remaining cup of sugar and 1 tablespoon vanilla. Beat on medium speed just until light and fluffy. Slowly beat in the heavy cream/coffee mixture until blended; take care to not over whip! Spoon the batter into prepared springform pan.
Place the springform pan in a large shallow pan containing hot water that comes about halfway up of the springform pan. Bake the cheesecake for about 1 hour and 10 minutes - the outside of the cake will set but the center will still be loose. Remove the cake from the water bath and let cool in the pan, on a wire rack, for 2 hours. Cover with plastic wrap and refrigerate until completely cold, preferably overnight or at least 4 hours.
Top the cold cheesecake, still in the pan, with a layer of 12 ladyfingers dipped in the coffee mixture. Transfer the cake to the freezer until completely frozen, 3-4 hours or overnight.
In a medium-size bowl, whip the 1 1/2 cups cream with the mixer on high speed until it thickens and soft peaks begin to form. With the mixer still running, add 2 tablespoons sugar and beat until the stiff peaks form. Do not over mix! Beat in 1 tablespoon vanilla. Gently fold in 8 oz. mascarpone with a rubber spatula.
Remove the cheesecake from the freezer and let it stand at room temperature for about 10 minutes. Spoon the 2/3 of the mascarpone mixture on the top of the cheesecake and even out with a frosting spatula. Since the cheesecake is still very cold, the mascarpone cream will set fast. Release and gently remove the sides of the springform. Spread the remaining mascarpone cream around the sides of the cake.
To decorate, sprinkle with cocoa powder or chocolate curls. Refrigerate at least 2 hours, until the mascarpone layer is cold and cheesecake layer has defrosted. Slice cake with a sharp straight-edge knife cleaning it with a paper towel between each slice. Keep leftover cake covered in a refrigerator for up to one week or freeze for up to one month.