Make the crust: Melt the butter in a microwave-safe bowl in 30-second bursts (30 seconds, stir, 15 more if needed). In a medium bowl, stir together the melted butter and the gluten-free graham cracker crumbs until all crumbs are moistened. Dump the mixture into the parchment-lined dish and press it into an even layer with the back of a spatula or a flat-bottomed measuring cup. Press firmly — loose crumbs will fall apart when you cut the bars.
Mix the pumpkin batter: In a large bowl, combine the pumpkin puree, heavy cream, 2 eggs, 2/3 cup sugar, 1 teaspoon vanilla, cinnamon, nutmeg, ginger, and cloves. Use a hand mixer on medium speed — or a stand mixer with the paddle attachment — and beat until smooth, about 45 seconds. No lumps allowed here. Pour the batter over the crust and spread it all the way to the edges with a spatula.
Mix the cheesecake batter: In a medium bowl, combine the softened cream cheese, 1 egg, the remaining 1/3 cup sugar, and 1 teaspoon vanilla. Beat with the hand mixer (or stand mixer) on medium speed until smooth and no streaks remain — about 30 seconds. Do not overbeat, or the cream cheese will get too airy and cause cracks later.
Swirl it together: Dollop spoonfuls of the cheesecake batter randomly over the pumpkin layer. Take a table knife and gently drag it through the dollops in a figure-eight motion — just two or three passes. Stop when you see pretty swirls; if you keep going, the two layers will blend into one.
Bake: Place the dish in the preheated oven and bake for 40 minutes. The edges should look set and slightly puffed, and the center will jiggle when you nudge the pan — that's okay. Resist the urge to bake it until the center is completely firm, or it will crack.
Cool: Remove the dish from the oven and set it on a wire rack. Let it cool at room temperature for exactly one hour — set a timer so you don't forget. Then transfer the dish to the refrigerator and chill for at least two hours, preferably three. This step is crucial for clean slices.
Slice and serve: Once fully chilled, grab the overhanging parchment paper and lift the entire slab out of the dish. Set it on a cutting board and use a sharp chef's knife to cut it into 12 bars (3 rows by 4 rows). Wipe the knife between cuts for the cleanest look. Serve cold or at room temperature.