Preheat the oven to 350℉/175℃. Grease and flour a 9×13-inch baking
pan.
Beat eggs in a stand mixer fitted with the whisk attchment on high
speed until thick and lemon-colored, about 3 minutes. Gradually add
sugar, beating until mixture is thick, about 5 minutes. Fold flour,
baking powder, and salt into the batter by hand.
Microwave milk in a microwave-safe bowl until it begins to bubble,
about 1 minute. Add butter and stir until melted. Stir in vanilla.
Pour hot milk miixture into the batter; blend onn low speed until
well combined and smooth. Pour into the prepared pan.
Bake in the preheated oven until a toothpick inserted in the center
comes out clean, 25 to 30 minutes.