Line an 8 x 8-inch baking pan with parchment paper.
In a small saucepan over low heat, melt the butter and white chocolate together, stirring for about 10 minutes until smooth. Remove from the heat and set aside.
In a large bowl, whisk together the granulated sugar and brown sugar.
Add the eggs and vanilla and stir to combine.
Slowly whisk the melted chocolate mixture into the egg mixture until fully combined.
Stir in the ube halaya and ube extract until evenly incorporated.
Add the flour, cocoa powder, and salt, and stir until combined.
Pour the batter into the prepared pan and bake for 30 minutes or until a toothpick inserted comes out with moist crumbs.
Let cool completely in the pan before slicing and serving.