Preheat your oven to 350°F (175°C). Line a 9x13 inch baking pan with parchment paper, leaving an overhang on the sides to easily lift the brownies out later. Lightly grease the parchment paper or spray with non-stick spray.

In a large microwave-safe bowl or a small saucepan, melt the unsalted butter. Once melted, stir in the granulated sugar until well combined. The mixture should be warm.

Add the 3 large eggs and 1 egg yolk to the butter-sugar mixture, one at a time, whisking vigorously after each addition for about 30 seconds. This incorporates air and helps create a chewy texture. The mixture should be thick and glossy.

Stir in the ube extract, softened ube halaya, and vanilla extract until the mixture is uniformly purple and smooth.

In a separate medium bowl, whisk together the all-purpose flour and salt.

Gradually add the dry ingredients to the wet ingredients, folding gently with a rubber spatula until just combined. Be careful not to overmix, as this can lead to dry brownies. Fold in the white chocolate chips, if using.

Pour the brownie batter into the prepared baking pan and spread evenly with the spatula.

Bake for 25-30 minutes, or until a toothpick inserted into the center comes out with moist crumbs, but not wet batter. The edges should be set, but the center might still look slightly soft for that fudgy texture.

Remove the pan from the oven and let the brownies cool completely in the pan on a wire rack for at least 2-3 hours, or even better, overnight. This is crucial for fudginess and clean cuts.

Once completely cooled, use the parchment paper overhang to lift the brownies out of the pan. Cut into 16 squares and serve.