Step 1: Preheat your oven to 325°F (160°C). Line an 8x8 or 9x9-inch baking pan with parchment paper, leaving an overhang on two sides.
Step 2: In a medium bowl, combine graham cracker crumbs, ¼ cup granulated sugar, and melted butter. Mix until well combined.
Step 3: Press the mixture firmly into the bottom of the prepared baking pan. Bake for 8-10 minutes, then remove and cool slightly.
Step 4: In a large mixing bowl, beat softened cream cheese on medium speed until smooth and creamy, about 2-3 minutes.
Step 5: Gradually add ¾ cup granulated sugar, beating until well combined and fluffy.
Step 6: Beat in the ube halaya, ube extract (if using), and vanilla extract until the mixture is uniformly purple and fragrant.
Step 7: Add the eggs one at a time, beating on low speed just until each egg is incorporated. Do not overmix.
Step 8: Stir in the heavy cream until just combined.
Step 9: Pour the ube cheesecake filling evenly over the partially baked crust. Gently tap the pan to release air bubbles.
Step 10: Bake for 30-35 minutes, or until the edges are set but the center still has a slight jiggle. Do not overbake.
Step 11: Remove from the oven and cool completely on a wire rack. Cover and refrigerate for at least 4 hours, or preferably overnight.
Step 12: Use the parchment paper overhang to lift the bars out of the pan. Slice into 16 or 25 even squares using a sharp knife. Serve cold.