Mix the dry ingredients. In a medium bowl, whisk the flour, baking powder, and salt. Set aside.
Beat the eggs. In a separate bowl, using an electric mixer, beat the sugar with the eggs until fluffy and pale, about 2 to 3 minutes.
Combine. Whisk the milk and vanilla into the egg mixture until smooth. Using a spatula, gently fold in the flour mixture just until the batter is smooth and lump-free.
Bake the cake. Grease your 9x13-inch baking dish with some butter. Pour in the prepared cake batter and tap gently onto the kitchen counter to remove air bubbles. Bake the cake for 30-35 minutes, or until a toothpick inserted into the center comes out clean.
Prepare the milk mixture:
Combine the milks. Meanwhile, whisk together the condensed milk, evaporated milk, and plain milk in a bowl until combined.
Drizzle the cake. Remove the cake from the oven and allow it to cool down completely. Then, use a fork to poke holes in the cake. Pour the milk mixture all over the cake, especially saturating the edges, as they are the firmest. Refrigerate the cake for at least 2 to 3 hours, but overnight is best.
Add the topping:
Whip the cream. Add heavy cream, powdered sugar, and vanilla extract to a large bowl. Whip with a handheld mixer until stiff peaks form.
Finish and serve. Top the tres leches cake with the whipped cream. Cut the cake into squares and serve.
Notes
Don't burn the cake. The cake top turns golden brown once baked. If you feel the cake is browning too quickly or too much during baking, you can cover it with aluminum foil and continue baking until done.
Carefully poke the cake. Use a fork to poke holes evenly across the cake. Avoid poking too many holes as it can ruin the cake's texture.
Beat your eggs with sugar until fluffy and pale. This is a very important step.
Instead of condensed milk, you can use dulce de leche and increase plain milk (in the milk mixture) from 3 tablespoons to a full ¼ cup. This will give the cake a caramel flavor.