Step 1: Preparation – Preheat your oven to 350°F (175°C). Line an 8×8 inch square baking pan with parchment paper, leaving an overhang on the sides to easily lift the bars out later. Lightly grease the parchment with non-stick spray.
Step 2: Prepare the Brownie Batter – In a large mixing bowl, combine the melted butter and 1 cup of sugar. Stir in the molasses, one egg, and 1 teaspoon of vanilla extract until the mixture is smooth. In a separate bowl, whisk together the flour, ginger, cinnamon, cloves, salt, and baking soda. Gradually add the dry ingredients to the wet ingredients, stirring until just combined. Fold in the chocolate chips.
Step 3: Layer the Base – Reserve about 1/4 cup of the gingerbread brownie batter and set it aside. Spread the remaining batter evenly into the bottom of your prepared baking pan. Use a spatula to smooth it out into the corners.
Step 4: Mix the Cheesecake Layer – In a medium bowl, beat the softened cream cheese and 1/4 cup of sugar until creamy and free of lumps. Add the remaining egg and 1/2 teaspoon of vanilla extract. Mix on low speed until the filling is smooth and fully incorporated.
Step 5: Swirl and Bake – Pour the cheesecake mixture over the brownie base in the pan. Drop small dollops of the reserved 1/4 cup brownie batter over the top of the cheesecake layer. Use a butter knife or a skewer to gently swirl the two layers together to create a marble pattern. Bake for 25 to 30 minutes, or until the edges are golden and the center is set.
Step 6: Cool and Slice – Remove the pan from the oven and let it cool completely on a wire rack. For the best results and cleanest cuts, refrigerate the bars for at least 2 hours before lifting them out of the pan and slicing them into 16 squares.