Step 1: Preheat your oven to 350°F (175°C). Grease and flour a 9x13 inch baking pan.
Step 2: In a medium bowl, whisk together the sifted flour, baking powder, and salt. Set aside.
Step 3: In a large bowl, using an electric mixer, beat the egg yolks with ½ cup of the granulated sugar until pale and creamy. Stir in the ½ cup whole milk, 1 tsp vanilla extract, and 1 tsp ube extract until well combined.
Step 4: Gradually add the dry ingredients to the egg yolk mixture, mixing on low speed until just combined. Do not overmix.
Step 5: In a separate clean bowl, beat the egg whites on medium-high speed until soft peaks form. Gradually add the remaining ½ cup of granulated sugar, beating until stiff, glossy peaks form.
Step 6: Gently fold one-third of the whipped egg whites into the batter to lighten it, then carefully fold in the remaining egg whites until no streaks remain. Be careful not to deflate the mixture.
Step 7: Pour the batter into the prepared baking pan and spread evenly. Bake for 30-35 minutes, or until a toothpick inserted into the center comes out clean. Let the cake cool in the pan for 15 minutes on a wire rack.
Step 8: While the cake cools, prepare the ube tres leches soak. In a large bowl, whisk together the sweetened condensed milk, evaporated milk, coconut milk, and 1 tsp ube extract. Add more ube extract if you desire a stronger flavor/color.
Step 9: Once the cake has cooled slightly, poke holes all over the top with a fork or skewer. Slowly and evenly pour the milk mixture over the entire cake. The cake will absorb the liquid. Cover the cake with plastic wrap and refrigerate for at least 4 hours, or preferably overnight, to allow it to fully soak.
Step 10: Before serving, prepare the whipped cream topping. In a very cold bowl with cold heavy cream, beat on medium-high speed until soft peaks form. Add the powdered sugar and 1 tsp vanilla extract, and continue beating until medium-stiff peaks form.
Step 11: Spread the whipped cream evenly over the chilled Ube Tres Leches Cake. Garnish with toasted coconut flakes or fresh fruit, if desired. Slice and serve cold.