In a food processor, combine chocolate cookies, semisweet chocolate pieces, brown sugar, and cinnamon. Cover and process until finely ground. Add melted butter; cover and process until combined. Press mixture onto the bottom and 2-1/2 inches up the side of an ungreased 10x3-inch springform pan. Set aside.
In a medium saucepan, bring whipping cream just to boiling over medium-high heat. Remove from heat. Add bittersweet chocolate; do not stir. Let stand for 5 minutes. Whisk until smooth. Whisk in coffee liqueur. Pour 2 cups of the ganache into crust, spreading evenly. Cover and freeze for 30 minutes. Transfer the remaining ganache to a small bowl; cover and chill until ready to serve. Preheat oven to 350 degrees F. In a very large bowl, combine cream cheese, the 1-1/3 cups granulated sugar, and the flour. Beat with an electric mixer on medium to high speed until smooth. In a small bowl, combine coffee powder, rum, the 1 tablespoon vanilla, and the molasses; stir to dissolve coffee powder. Add to cream cheese mixture; beat until combined. Stir in eggs. Pour over ganache layer in pan, spreading evenly.
Place cheesecake on a foil-lined large baking sheet. Bake for 60 to 70 minutes or until a 3-inch area around the outside edge appears set and the center appears nearly set when gently shaken.
Meanwhile, in a medium bowl, stir together sour cream, the 1/3 cup granulated sugar, and the 2 teaspoons vanilla. Pour over hot cheesecake, spreading to cover filling. Bake about 10 minutes more or until topping is set. Cool cheesecake in pan on a wire rack for 15 minutes. Using a small sharp knife, loosen the crust from side of pan. Cool completely (about 1-3/4 hours). Remove side of pan. Cover and chill overnight. Let cheesecake stand at room temperature for 30 minutes before serving. Heat the remaining ganache. Spoon ganache over each serving of cheesecake
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