Preheat oven to 350 degrees F (175 degrees C). Grease a 9x13-inch baking dish.
Beat brown sugar and butter together in a bowl using an electric mixer until smooth and creamy. Add 1 egg, 1 teaspoon vanilla extract, and almond extract; mix until combined. Stir flour and salt into creamed mixture until crust mixture is well combined; fold in white chocolate chips and dried cranberries. Press crust mixture into the prepared baking dish.
Beat sweetened condensed milk and cream cheese together in a bowl using an electric mixer until well combined. Add 2 eggs, lemon zest, and 1 teaspoon vanilla extract; beat well. Spread cream cheese mixture over crust mixture.
Whisk cherry preserves in a small bowl until runny. Drop spoonfuls of cherry preserves over cream cheese mixture layer. Lightly draw a knife through cream cheese mixture creating a swirling pattern.
Bake in the preheated oven until cheesecake is lightly browned and crust pulls away from sides of dish, 35 to 40 minutes. Cool and refrigerate before serving, at least 1 hour.