Preheat oven to 325°F (165°C) and line a 9x9-inch baking pan with parchment paper. Mix cookie crumbs, brown sugar, cinnamon, and melted butter; press firmly into the pan and bake for 10 minutes.
Beat softened cream cheese and granulated sugar until smooth. Mix in sour cream and vanilla, then add eggs one at a time on low speed.
Pour two-thirds of the vanilla cheesecake batter over the crust. Whisk pumpkin purée, brown sugar, flour, and pumpkin pie spice into the remaining one-third of the batter.
Dollop the spiced pumpkin batter over the vanilla layer and swirl with a butter knife. Bake at 325°F for 36–40 minutes until edges are set. Cool for 1 hour, then chill for 3 hours before slicing into 16 bars.