4 tablespoons unsalted butter
1/2 cup whole milk
1 1/2 cups bleached all-purpose flour (spoon flour into dry-measure cup and level off)
2 teaspoons baking powder
3 large eggs, at room temperature
1/4 teaspoon salt
1 cup sugar
1 teaspoon vanilla extract
Two 9-inch round cake pans, 1 1/2 to 2 inches deep, buttered and the bottoms lined with disks of parchment paper or buttered wax paper
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Set a rack in the middle level of the oven and preheat to 350˚F.
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Combine the butter and milk in a small saucepan and cook over low heat until the butter is completely melted. Set aside in the pan.
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Stir the flour and baking powder together and sift onto a piece of wax paper.
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In the bowl of an electric mixer, whisk the eggs by hand to break them up, then whisk in the salt. Whisk in the sugar in a stream, then whisk in the vanilla. Place on the mixer fitted with the whisk attachment and whip on medium-high speed until very light, about 3 minutes.
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Gently whisk in the warm milk mixture by hand. Use the whisk to fold the flour mixture into the liquid in 4 additions, again gently whisking to incorporate between additions. Using the whisk helps to prevent lumps from forming. Handle the whisk exactly as though you were using a rubber spatula for the folding.
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Evenly divide the batter between the prepared pans and smooth the tops.
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Bake the layers until they are well risen and golden and feel firm when touched in the center with a fingertip, about 20 minutes.
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Use a sharp paring knife to loosen the layers from the sides of the pans, then invert to racks. Immediately re-invert the layers so that they cool with the paper on the bottom. Cool completely.
