1. Preheat oven to 325 degrees. Butter two 9-by-13-inch baking pans. Line with parchment, leaving an overhang on long sides. Butter parchment. Flour pans, tapping out excess.

2. Sift together flour, baking powder, and salt. Beat together butter and sugar in a large bowl until light and fluffy, about 3 minutes. Add vanilla, then beat in eggs, 1 at a time.

3. Beat flour mixture into butter mixture in 3 additions, alternating with milk, beginning and ending with flour mixture. Scrape bottom of bowl, and mix until smooth. Divide batter between pans.

4. Bake, rotating halfway through, until tops of cakes spring back when pressed and a toothpick comes out clean, 40 to 45 minutes. Let cool completely, then lift cakes from pans using parchment. Remove parchment. Cakes can be wrapped in plastic wrap and kept at room temperature 1 day or refrigerated 2 days.