Preheat your oven to 350°F (175°C). Grease a Twinkie pan or mini loaf pan and set aside.
In a small bowl, sift together the flour, baking powder, and salt.
In a large bowl, beat the eggs and sugar with an electric mixer until the mixture becomes thick, pale, and fluffy, about 6–8 minutes.
Add the vanilla extract and gently mix to combine.
Fold the dry ingredients into the egg mixture in small batches, mixing gently to keep the batter light and airy.
In a separate bowl, combine the warm milk and melted butter. Fold this mixture carefully into the batter until just incorporated.
Fill each mold about three-quarters full with batter.
Bake for 12–15 minutes, or until the cakes are lightly golden and a toothpick inserted in the center comes out clean.
Allow the cakes to cool completely before removing them from the pan.