Preheat oven to 325°F (160°C). Grease a 9-inch springform pan.

For the crust: Combine graham cracker crumbs, brown sugar, and cinnamon in a bowl. Stir in melted butter until well combined. Press mixture firmly into the bottom of the prepared springform pan. Bake for 10 minutes, then set aside.

For the filling: In a large bowl, beat softened cream cheese and granulated sugar with an electric mixer until smooth and creamy.

Beat in the flour, then vanilla extract, until just combined.

Divide the cream cheese mixture evenly into two separate bowls.

In the first bowl, add ube extract (if using) and ube halaya. Mix until well combined and the batter is a vibrant purple color.

In the second bowl, add pumpkin puree and pumpkin pie spice. Mix until well combined.

Pour the ube batter into the prepared crust. Gently spoon the pumpkin batter over the ube layer. Using a knife or skewer, gently swirl the two batters together to create a marbled effect.

Bake for 50-60 minutes, or until the edges are set but the center still jiggles slightly. Turn off the oven, crack the door open, and let the cheesecake cool inside for 1 hour.

Remove from oven and let cool completely on a wire rack. Once cooled, cover and refrigerate for at least 6 hours, or preferably overnight, before serving. Carefully remove the springform pan and slice. Serve chilled.