Heat the oven to 350°F (175°C). Grease an 8-inch (20-cm) round cake pan and line the base with parchment paper so the finished cake releases easily.

Whisk the flour, baking powder, and fine salt together in a medium bowl. This spreads the leavening and salt evenly throughout the flour before it is added to the wet mixture.

Beat the softened butter and granulated sugar for 3–4 minutes, until pale, airy, and fluffy. Scrape the bowl once or twice so the mixture becomes evenly creamy.

Add the eggs one at a time, beating well after each addition. Mix in the vanilla extract, stopping to scrape down the sides of the bowl if needed.

Add the dry ingredients in three additions, alternating them with the milk in two additions. Mix only until the batter is smooth, because overmixing can make the cake dense or chewy.

Transfer the batter to the prepared pan and smooth the top with a spatula. Bake for 30–35 minutes, beginning to check a few minutes early.

The cake is ready when the center springs back lightly and a toothpick inserted in the middle comes out clean or with a few moist crumbs. Cool it in the pan for 10–15 minutes, then transfer it to a rack to cool completely.