Preheat the oven to 325°F.

Line an 8×8-inch baking pan with parchment paper.

Melt the butter, then combine it with the graham cracker crumbs, 2 tablespoons granulated sugar, and 2 tablespoons brown sugar. Press the mixture firmly into the bottom of the prepared pan.

In a large bowl, beat the cream cheese with the remaining granulated and brown sugars until smooth. Mix in the sour cream and vanilla, then add the eggs one at a time, mixing just until combined.

Transfer 1½ cups of the cheesecake batter to a separate bowl. Stir in the pumpkin purée and pumpkin pie spice.

Drop alternating spoonfuls of the plain and pumpkin cheesecake batters over the crust, then gently swirl them together with a knife or toothpick.

Bake for 45–50 minutes, until the edges are set and the center still has a slight jiggle.

Cool completely at room temperature, then refrigerate for at least 6 hours, or overnight, before slicing and serving.