Preheat your oven to 350°F (175°C). Grease and flour a 9x13 inch baking dish.
In a medium bowl, whisk together the flour and baking powder. Set aside.
In a large bowl, beat the egg yolks with 3/4 cup of granulated sugar until pale and fluffy. Mix in the vanilla extract and whole milk.
Gradually add the flour mixture to the egg yolk mixture, mixing until just combined.
In a separate bowl, beat the egg whites until soft peaks form. Gradually add the remaining 1/4 cup of sugar and continue to beat until stiff peaks form.
Gently fold the egg whites into the batter until no streaks remain.
Pour the batter into the prepared baking dish and bake for 25-30 minutes, or until a toothpick inserted into the center comes out clean. Let the cake cool completely.
In a large bowl, whisk together the sweetened condensed milk, evaporated milk, and whole milk until well combined.
Once the cake has cooled, poke holes all over the top using a fork. Slowly pour the milk syrup over the cake, allowing it to soak in. Cover and refrigerate for at least 2 hours, or overnight.
In a medium saucepan, combine the granulated sugar and water. Cook over medium heat, stirring occasionally, until the sugar has dissolved.
Increase the heat to high and cook without stirring until the mixture turns a deep amber color. Remove from heat and carefully whisk in the heavy cream, butter, and vanilla extract. Be cautious as the mixture will bubble up.
Allow the caramel to cool slightly before pouring it over the soaked cake.
Cut the Trilece into squares and serve chilled.
Enjoy your meal!