Preheat your oven to 350°F (175°C). Grease and flour a 9x13-inch baking pan.
Combine the flour, baking powder, baking soda, and salt in a bowl and whisk them together.
In another bowl, beat the eggs and sugar together until light and fluffy, about 5 minutes. Stir in the vanilla extract.
Slowly incorporate the dry ingredients into the egg mixture, stirring until they are just blended together. Pour the batter into the prepared pan.
Bake for 30-35 minutes or until a toothpick inserted into the center comes out clean.
While the cake is baking, combine the three milks in a separate bowl.
Once the cake is out of the oven, poke it all over with a fork or skewer.
Pour the milk mixture evenly over the warm cake. Allow it to soak for at least 30 minutes.
In a cold mixing bowl, beat the heavy cream, confectioners' sugar, and vanilla extract until they form stiff peaks.
Spread the whipped cream over the soaked cake and refrigerate for a few hours before serving.