Preheat oven to 350 F (175 C). Grease a 9x5-inch (23x13-cm) loaf pan with nonstick spray and line with parchment paper so there is overhang on both long sides.
In a medium bowl, whisk together the flour, baking powder, baking soda, and salt.
In the bowl of a stand mixer fitted with the paddle, add the butter and sugar. Beat on medium speed until light and fluffy, about 4 minutes. Beat in the eggs one at a time. Beat in the bananas.
Add the flour mixture in two additions, beating on low speed until mostly combined but not quite. Finish mixing with a rubber spatula.
In a medium bowl, whisk together the ube halaya, milk, and ube paste until smooth. Add 1 ½ cups (360g) of the banana batter and fold until just combined. Do not overmix.
Add the batters, in alternating dollops, to the prepared pan (I usually do about 3 tablespoons per dollop).
Using a butter knife, swirl the batter to create a marbled pattern. Tap the pan firmly against the counter a few times.
Bake on a sheet pan until golden and a long skewer inserted into the center of the cake comes out clean, about 1 hour 25 minutes to 1 hour 35 minutes (a few sticky crumbs are okay). Cover loosely with foil for the last 30 minutes to prevent over-browning.
Transfer pan to a wire rack and let cool for 20 minutes. Remove bread from pan and set on rack. Let cool completely.
