Preheat the oven to 350 degrees F. Line a 9X13-inch metal baking pan with parchment paper with overhang on both long sides (to easily remove the bars). Grease the parchment paper and sides of pan with nonstick cooking spray. If using a glass pan, you might want to reduce the oven temperature by 25 degrees.
For the cookie dough, in the bowl of an electric stand mixer or with a handheld electric mixer, cream together the butter, granulated sugar and brown sugar, until light and fluffy, 2-3 minutes. Add the molasses and eggs and mix until well combined.
Add the flour, cinnamon, ginger, baking powder, baking soda, salt, nutmeg, allspice, and cloves, and mix until no dry streaks remain (don't over mix).
Reserve 2 cups of the dough (about 20 ounces) and set aside. Press the remaining dough in the bottom of the prepared pan.
For the cheesecake layer, in the bowl of an electric stand mixer or with a handheld electric mixer, beat the cream cheese until smooth. Add the sugar and flour and mix until well-combined, 1-2 minutes, scraping down the sides of the bowl as needed. Add the eggs and vanilla and mix until combined.
Spread the cheesecake batter over the gingerbread cookie dough in the pan. Crumble the reserved gingerbread cookie dough over the top of the cheesecake layer in small pieces.
Bake for 45-55 minutes until the edges are set - cover the top loosely with foil after the first 30 minutes to prevent the cookie dough from browning too much on top. The center may still jiggle slightly, that's ok. An instant-read thermometer inserted in the center should read 175 to 180 degrees F.
Let the bars cool completely in the pan. Cover and refrigerate for at least 4 hours or up to 12 hours. Remove the bars from the pan, cut into squares and serve.
Notes
Molasses: black strap molasses are too strong for this recipe and the thicker consistency will affect the texture of the bars.Freezing: these bars, once cut into squares, freeze really well.Cookie Dough: if you find that the cookie dough seems over baked or hard when the bars come out of the oven, don't worry! The cookie dough softens beautifully once the bars cool and after they are covered and chilled.