Preheat the oven to 350 degrees with the rack you'll be baking on in the bottom third of the oven.
Spray an 8x8x2 square baking pan with cooking spray.
In a small bowl, whisk together the flour and baking powder.
In a stand mixer fitted with the paddle attachment, add the eggs, egg yolks, sugar, vanilla and salt. Beat this mixture on high until very pale and fluffy, 4-6 minutes.
Meanwhile, heat the milk and butter together in a glass bowl or measuring cup in the microwave (about 2 minutes) until melted and hot, but not boiling.
Once the egg mixture is pale and fluffy, sift the flour and baking powder mixture into it in three separate additions, mixing gently with a spatula after each addition.
Then pour the hot milk and butter on top of the cake batter and stir until well combined.
Pour the batter into the prepared pan. Tap the pan on the counter to burst any air bubbles.
Bake 20-25 minutes until top of cake springs back easily when lightly touched.
Allow to cool and then slice into squares.