Step 1

Place 3 large eggs in the bowl of a stand mixer (or large bowl if using an electric hand mixer). Let sit until room temperature. Meanwhile, arrange a rack in the middle of the oven and heat the oven to 325ºF.

Step 2

Coat the sides and bottoms of 1 (9-inch) square cake pan, or 2 (9-inch) round cake pans with butter. Line the bottom of each pan with parchment paper. Sprinkle a little all-purpose flour over the sides and bottoms, and tilt and shake to distribute evenly, tapping out the excess.

Step 3

Place 1 1/4 cups all-purpose flour and 2 teaspoons baking powder in a medium bowl and whisk to combine. Cut 6 tablespoons unsalted butter into small cubes and place in a microwave-safe measuring cup. Add 3/4 cup whole milk and microwave in 30-second intervals, stirring in between each, until the butter is melted, 60 to 90 seconds total. (Alternatively, heat the butter and milk in a small saucepan over medium heat.) Add 2 teaspoons vanilla extract and 1/2 teaspoon kosher salt, and stir to combine.

Step 4

Add 1 1/4 cups granulated sugar to the bowl of eggs. Beat with the whisk attachment on high speed until thick and doubled in volume, about 6 minutes. The mixture should fall back on itself in a ribbon and be pale yellow in color. Reduce the mixer speed to low and pour in the milk mixture in a steady stream. Add the flour mixture, a few spoonfuls at a time, and beat, scraping down the sides of the bowl halfway through, until just combined, about 30 seconds total.

Step 5

Pour the batter into the pan. Bake until the cake is a light golden brown and until a tester inserted in the center of each cake comes out clean, about 30 minutes.

Step 6

Evenly divide the batter between the pans (about 14 ounces or 2 3/4 cups each). Bake until the cakes are a light golden brown and until a tester inserted in the center of each cake comes out clean, 22 to 25 minutes.

Step 7

Place the pan(s) on a wire rack and let cool for 15 minutes. Run a small offset spatula or thin knife around the edges of each cake to loosen. Flip the cakes out of the pan(s) onto the rack and remove the parchment paper. Gently flip right side up, and let cool completely, about 30 minutes.