Preheat oven to 325°. Stir together crushed graham crackers, butter, and 1 Tbsp. sugar. Press mixture on bottom and halfway up sides of a 9-inch springform pan. Freeze 10 minutes.
Beat cream cheese, 1 1/4 cups sugar, and cornstarch at medium speed with an electric mixer 2 to 3 minutes or until smooth. Add eggs, 1 at a time, beating at low speed just until yellow disappears after each addition. Add 3 Tbsp. brandy and 3 Tbsp. crème de cacao, and beat just until blended. Pour into prepared crust.
Bake at 325° for 1 hour or just until center is almost set.
During last 2 minutes of baking, stir together sour cream and remaining 1 Tbsp. sugar, 1 Tbsp. brandy, and 1 Tbsp. crème de cacao.
Spread sour cream mixture over cheesecake. Bake at 325° for 8 more minutes. Remove cheesecake from oven; gently run a knife along outer edge of cheesecake, and cool completely in pan on a wire rack (about 1 1/2 hours). Cover and chill 8 to 24 hours.
Remove sides of springform pan, and place cheesecake on a serving plate. Garnish, if desired.
*Coffee liqueur may be substituted. We tested with Kahlúa.
Note: We tested with Nabisco Teddy Grahams chocolate graham snacks.
To freeze up to one month, wrap springform pan tightly with aluminum foil, and slide into a zip-top plastic freezer bag.