Let's cook.
Preheat oven to 325°F (160°C). Line an 8x8 inch baking pan with parchment paper, leaving an overhang on two sides.
In a medium bowl, combine the crushed graham crackers and melted butter. Press the mixture evenly into the bottom of the prepared baking pan to form the crust.
In a large bowl, beat the softened cream cheese and granulated sugar with an electric mixer until smooth and creamy. Beat in the eggs one at a time, then stir in the vanilla extract.
Divide the cream cheese mixture into two equal portions. In one portion, gently fold in the ube halaya and ube extract (if using) until well combined and a uniform purple color is achieved.
Pour the plain cream cheese mixture over the graham cracker crust. Carefully spoon dollops of the ube cream cheese mixture over the plain layer. Use a knife or skewer to gently swirl the two mixtures together for a marbled effect.
Bake for 40-45 minutes, or until the edges are set and the center is still slightly jiggly. Do not overbake.
Remove from oven and let cool completely on a wire rack. Once cooled, refrigerate for at least 4 hours, or preferably overnight, before slicing into bars.
Lift the parchment paper to remove the cheesecake from the pan, then slice into 12 bars.
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