Step 1: Preheat your oven to 350°F (175°C). Grease and flour a 9×13 inch baking pan, then line the bottom with parchment paper.
Step 2: In a medium bowl, sift together the cake flour, baking powder, and salt. Set aside.
Step 3: In a large mixing bowl, cream together the softened butter and 1 cup of granulated sugar until light and fluffy.
Step 4: Beat in the egg yolks one at a time, mixing well after each addition. Stir in the vanilla extract and 1 teaspoon of ube extract.
Step 5: Gradually add the dry ingredients to the wet ingredients, alternating with the whole milk, beginning and ending with the dry ingredients. Mix until just combined, being careful not to overmix.
Step 6: In a separate, clean bowl, beat the egg whites with the remaining ½ cup of granulated sugar and a pinch of cream of tartar until stiff peaks form.
Step 7: Gently fold the whipped egg whites into the cake batter in two additions, until no streaks remain and the batter is light and airy.
Step 8: Pour the batter into the prepared baking pan and spread evenly. Bake for 25-30 minutes, or until a toothpick inserted into the center comes out clean. Let the cake cool in the pan for 10 minutes, then invert it onto a wire rack to cool completely. Once completely cool, poke holes all over the cake using a fork or a skewer.
Step 9: While the cake cools, prepare the tres leches soak. In a large bowl, whisk together the evaporated milk, sweetened condensed milk, and ½ cup of heavy cream. Add the ube halaya and whisk until fully dissolved and incorporated, creating a beautiful purple milk mixture.
Step 10: Slowly and evenly pour the ube tres leches mixture over the cooled, poked cake. Ensure the entire surface is covered so the cake absorbs the liquid thoroughly.
Step 11: Cover the cake with plastic wrap and refrigerate for at least 4 hours, or preferably overnight, to allow the cake to fully absorb the milks and chill thoroughly.
Step 12: To make the topping, in a cold bowl, whip the 2 cups of cold heavy cream with the powdered sugar and ½ teaspoon of ube extract until stiff peaks form.
Step 13: Spread the whipped cream evenly over the chilled ube tres leches cake. Garnish with toasted coconut flakes, ube crumbs, or fresh berries if desired, before serving.