1.Heat milk and butter in a small saucepan over medium, stirring, until butter is melted. Let cool.
2.Arrange a rack in center of oven; preheat to 350˚. Lightly coat a 9" round cake pan nonstick spray.
3.Whisk flour and baking powder in a small bowl. Sift through a fine-mesh sieve into a bowl.
4.Using an electric mixer on low speed, beat eggs in a large bowl, gradually increasing speed to medium-high, until combined. Add salt and continue to beat until mixture begins to foam, about 1 minute. Reduce mixer speed to low and gradually add sugar; increase speed to high and beat until very light and pale yellow, about 4 minutes.
5.Reduce mixer speed to low again and gradually add dry ingredients, and beat on medium speed until no lumps remain and batter is very thick. Beat in vanilla and cooled milk mixture just until combined. Scrape sides and bottom of bowl with a spatula, give batter a good stir with spatula, then scrape into prepared pan.
6.Bake cake until top is golden and a tester inserted into the center comes out clean, 15–25 minutes. Let cool.