Set the oven to 325°F and grease a 9x13-inch pan at least 2 inches deep, or line the bottom of a 13x18-inch half-sheet pan with parchment and grease its sides. The deeper pan produces thicker squares; the half-sheet produces a thinner layer.

Whip the eggs with the sugar using an electric mixer at medium-high speed for about 2 minutes, then gradually beat in the oil. Before adding the oil, look for a pale, fluffy mixture that falls from the beaters in thick ribbons.

Weigh the flour, or spoon it gently into a measuring cup and level it, then add it with the salt and baking powder and beat only until incorporated. Scrape along the bowl’s sides and bottom, then mix briefly so no sticky pockets remain.

Heat the milk and butter in a saucepan over medium heat until boiling just begins, add the vanilla, then remove from the burner and stir until the butter melts. The liquid should look uniform, with no solid butter remaining.

Run the mixer on low and pour the hot liquid gradually into the batter, then scrape the bowl and mix briefly. A smooth, noticeably thin batter is the expected result.

Transfer the batter to the prepared pan and bake for 40 to 45 minutes for the 9x13-inch cake or 22 to 26 minutes for the half-sheet, rotating halfway through. The center should feel set, spring back gently, and release a toothpick without wet batter.

Move the baked cake, still in its pan, onto a cooling rack. The delicate crumb becomes easier to cut as the cake cools.