Preheat oven to 325 °F (163 °C). Grease a 9‑inch springform pan and line bottom with parchment.
Mix graham crumbs, ¼ cup sugar, and melted butter. Press into pan bottom and bake 8 minutes. Cool.
Beat cream cheese and 1 cup sugar until smooth. Add eggs one at a time, blending after each.
Mix in vanilla, sour cream, and heavy cream until silky.
Reserve 1 cup filling. Stir ube halaya (and extract, if using) into reserved portion until evenly purple.
Pour plain filling into crust, then dollop ube filling on top. Swirl gently with a knife.
Bake 50–60 minutes until edges are set but center slightly wobbles.
Turn off oven, crack door, and let cheesecake sit 1 hour.
Chill in fridge 4 hours or overnight before removing springform and slicing.