Step 1: Preheat your oven to 350°F (175°C). Line a 9x13 inch baking pan with parchment paper, leaving an overhang on the sides for easy lifting.
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 crumb mixture firmly and evenly into the bottom of the prepared baking pan. Bake for 8-10 minutes, then let cool slightly.
Step 4: In a large mixing bowl, beat the softened cream cheese on medium speed until smooth and creamy, about 2-3 minutes.
Step 5: Add 1 cup granulated sugar to the cream cheese and beat until well combined and fluffy, scraping down the sides of the bowl.
Step 6: Beat in the ube halaya and ube extract (if using) until fully incorporated and the mixture is uniformly purple.
Step 7: Add the eggs one at a time, beating on low speed just until each egg is incorporated. Gently fold in the heavy cream until just combined.
Step 8: Pour the ube cheesecake filling over the cooled graham cracker crust. Gently tap the pan on the counter a few times to release air bubbles.
Step 9: Bake for 30-35 minutes, or until the edges are set but the center still has a slight jiggle. Do not overbake.
Step 10: Turn off the oven, crack the oven door slightly, and let the Ube Cheesecake Bars cool in the oven for about 30 minutes. Then, remove and let cool completely on a wire rack at room temperature.
Step 11: Once completely cool, cover the pan and refrigerate for at least 4 hours, or preferably overnight, until fully firm.
Step 12: Use the parchment paper overhang to lift the cheesecake out of the pan. Place on a cutting board and cut into 16-24 bars using a warm, sharp knife.