To prepare almond cake, combine 6 tablespoons sugar, 1/4 cup butter, 1/8 teaspoon salt, and 4 ounces almond paste in a large bowl; beat with an electric mixer at medium speed until light and fluffy (about 3 minutes). Add 2 eggs, 1 at a time, beating well after each addition. Weigh or lightly spoon cake flour into a dry measuring cup; level with a knife. Stir flour and rum into sugar mixture. Spread the batter evenly into a 9-inch springform pan coated with cooking spray. Bake at 350° for 20 minutes or until a wooden pick inserted in center comes out clean. Cool completely in pan on a wire rack (do not remove or loosen sides of springform pan).
Reduce oven temperature to 300°.
To prepare the cheesecake, place softened cheeses, 1/2 cup sugar, and salt in a large bowl; beat with a mixer at medium speed just until blended. Add 3 eggs, 1 at a time, beating at low speed just until each addition is incorporated. Scrape seeds from vanilla bean, and reserve bean for another use. Add seeds, pumpkin, yogurt, and ginger to cream cheese mixture; beat at low speed just until blended. Pour the cream cheese mixture evenly over top of cooled almond cake. Bake at 300° for 1 hour or until cheesecake center barely moves when pan is touched. Remove cheesecake from oven, and run a knife around outside edge. Cool to room temperature on a wire rack. Cover and chill for 8 hours or overnight.
To prepare brittle, line a baking sheet with parchment paper; coat parchment paper with cooking spray. Combine 1/2 cup sugar, 1 1/2 tablespoons water, and corn syrup in a small saucepan; bring to a boil, stirring just until sugar dissolves. Cook, without stirring, for 7 minutes or until mixture is golden. Remove from heat. Stir in almonds and butter. Quickly spread sugar mixture in a thin, even layer over prepared parchment; cool completely. Break into 14 pieces. Slice cheesecake into 14 slices; top each serving with 1 tablespoon whipped topping and 1 piece brittle.