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Preheat your oven to 350°F (175°C). Line an 8-by-8-inch baking pan with parchment paper, leaving some overhang on the sides to make the finished bars easier to lift out.
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Mix the gingersnap crumbs, melted butter, brown sugar, cinnamon, and salt until the crumbs are evenly coated and resemble damp sand. Press the mixture firmly into the bottom of the prepared pan. Use the bottom of a glass or measuring cup to create an even layer.
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Bake the crust for 8–10 minutes, then set it aside while you prepare the fillings.
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In a medium bowl, whisk together the pumpkin puree, brown sugar, eggs, heavy cream, and vanilla until smooth. Add the cinnamon, ginger, nutmeg, cloves, and salt. Whisk just until everything is incorporated. Try not to overmix once the eggs are added. The filling should be smooth, creamy, and fragrant with warm spices.
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Place the softened cream cheese in another bowl and beat until smooth. Add the sugar, egg yolk, vanilla, and flour.
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Mix until creamy and lump-free. If your cream cheese is still cold, it may be difficult to get a smooth swirl, so letting it soften at room temperature beforehand makes a noticeable difference.
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Pour the pumpkin mixture over the slightly cooled gingersnap crust and spread it into an even layer.
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Spoon small dollops of the cream cheese mixture over the pumpkin layer. Using the tip of a butter knife or a skewer, gently swirl the cream cheese through the pumpkin filling. Don't over-swirl. A few deliberate passes will give you those pretty cream-colored ribbons without blending the two fillings together.
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Bake for 35–40 minutes, or until the edges look set and the center still has a slight jiggle when the pan is gently moved.
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Don't worry if the middle doesn't look completely firm when you take the bars out. They will continue setting as they cool and chill. Let the bars cool in the pan for about 1 hour.
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Once cooled, cover the pan and refrigerate for at least 3 hours, preferably longer. When you're ready to serve, lift the bars out using the parchment paper. Cut them into 16 squares with a sharp knife. For especially clean slices, wipe the knife between cuts.