Preheat oven to 350°F (175°C). Grease a baking pan.
In a mixing bowl, whisk together the gluten-free flour and baking powder.
In another bowl, beat the butter and sugar until fluffy. Add egg yolks and vanilla extract, mix well.
Gradually add the flour mixture to the butter mixture, mix until combined.
In a separate bowl, beat egg whites until stiff peaks form. Gently fold into the batter.
Pour the batter into the prepared pan. Bake for 30 minutes or until a toothpick comes out clean.
In a bowl, mix whole milk, evaporated milk, and sweetened condensed milk.
Once the cake is baked, poke holes all over it and pour the milk mixture evenly on top.
Refrigerate for at least 4 hours before serving.