Step 1: Preheat your oven to 350°F (175°C). Grease and flour a 9x13 inch baking pan. In a medium bowl, whisk together the all-purpose flour, baking powder, and salt. Set aside.
Step 2: In a large bowl, whisk the egg yolks with ½ cup of granulated sugar until pale and creamy. Stir in the whole milk, vegetable oil, and 2 teaspoons of ube extract. Gradually add the dry flour mixture to the wet ingredients, mixing until just combined. Be careful not to overmix.
Step 3: In a separate clean bowl, beat the egg whites with an electric mixer until soft peaks form. Gradually add the remaining ½ cup of granulated sugar, beating until stiff, glossy peaks form.
Step 4: Gently fold one-third of the beaten egg whites into the ube batter to lighten it, then carefully fold in the remaining egg whites until no streaks remain. Pour the batter into the prepared baking pan and spread evenly.
Step 5: Bake for 25-30 minutes, or until a wooden skewer inserted into the center comes out clean. Let the cake cool in the pan on a wire rack for about 15 minutes, then poke holes all over the top of the cake using a fork or skewer. This will allow the ube tres leches cake recipe to absorb the milk mixture efficiently.
Step 6: While the cake cools, prepare the tres leches milk soak. In a bowl, whisk together the evaporated milk, sweetened condensed milk, ½ cup heavy cream, and 1 teaspoon of ube extract until fully combined.
Step 7: Slowly and evenly pour the milk mixture over the entire surface of the warm, poked cake. Allow the cake to absorb the milk for at least 30 minutes at room temperature, then cover with plastic wrap and refrigerate for at least 4 hours, or preferably overnight, for the best absorption for your ube tres leches cake recipe.
Step 8: Just before serving, prepare the whipped topping. In a large cold bowl, beat the 2 cups cold heavy cream, ½ cup powdered sugar, and 1 teaspoon vanilla extract with an electric mixer on high speed until stiff peaks form.
Step 9: Spread the whipped topping evenly over the chilled ube tres leches cake. Garnish with toasted shredded coconut, fresh ube halaya, or fresh berries, if desired. Slice and serve cold. Store any leftover ube tres leches cake recipe in the refrigerator in an airtight container.