Prep Pan & Oven: Preheat your oven to 325°F (165°C). Line an 8x8-inch square metal baking pan with parchment paper, leaving an overhang on the sides for easy lifting after chilling.
Bake Gingersnap Crust: In a medium bowl, combine crushed gingersnap cookie crumbs, melted butter, and packed brown sugar. Press firmly into an even, compact layer across the bottom of the prepared pan. Bake for 10 minutes until fragrant and lightly set. Cool on a wire rack while preparing batters.
Make Cream Cheese Base: In a large stand mixer bowl fitted with the paddle attachment, beat softened cream cheese and granulated sugar on medium speed for 2 to 3 minutes until silky smooth and completely lump-free. Scrape down bowl sides.
Add Eggs & Vanilla: Beat in eggs one at a time on low speed, mixing just until incorporated. Stir in 1 teaspoon pure vanilla extract and sea salt. Do not overmix to prevent whipping excess air into the cheesecake.
Create Spiced Pumpkin Batter: Scoop out 1/2 cup of the plain cheesecake batter and set aside. To the remaining batter in the mixer bowl, add the pure pumpkin puree, ground cinnamon, ginger, nutmeg, cloves, and the remaining 1/2 teaspoon vanilla. Mix on low until fully blended into a rich spiced orange batter.
Assemble & Marble Swirl: Pour the spiced pumpkin cheesecake batter over the cooled gingersnap crust. Drop spoonfuls of the reserved plain vanilla batter evenly over the top. Use the tip of a butter knife or wooden skewer to gently swirl the batters together in figure-eight motions to create an artistic marbled pattern.
Bake to Gentle Wobble: Bake at 325°F (165°C) for 32 to 36 minutes, until the edges are set and puffy but the center still has a slight gentle jiggle when the pan is nudged.
Cool & Chill: Turn off the oven, crack the oven door open 2 inches, and let the cheesecake rest inside for 20 minutes to prevent surface cracking. Transfer pan to a wire rack to cool to room temperature, then cover loosely and refrigerate for at least 4 hours (preferably overnight). Slice into neat squares using a hot, wiped knife.