Preheat your oven to 350°F and ready a rack in the middle of the oven.
Lightly butter your pan, line it with parchment paper, and butter the paper. Then lightly flour the pan.
Sift or whisk the flour, baking powder, and salt together into a small bowl.
1½ cups ((180 grams)) cake flour, 1½ teaspoons baking powder, ¼ teaspoon salt
In the bowl of your stand mixer, or in a medium bowl if using a hand mixer, beat the butter and sugar together on medium speed until light and fluffy, about 3 to 5 minutes, scraping down the bowl as needed.
8 tablespoons ((113 grams)) unsalted butter, softened, 1 cup (200 grams) granulated sugar
Add the eggs one at a time and beat on medium for one minute after each addition, scraping down the bowl as needed.
2 large eggs, room temperature
Measure out the milk, add the vanilla to the measuring cup, and stir to combine.
½ cup whole milk, 1 teaspoon vanilla extract
Add one half of the dry ingredients to the butter, sugar, and egg mixture, and beat on low speed until just combined. Scrape down the bowl.
Add the milk and vanilla and mix on low. Then add the remaining dry ingredients and beat on low until just combined.
Scrape the batter into the prepared pan and bake for 30 to 35 minutes, until a toothpick inserted into the center comes out clean and the cake is just starting to pull away from the sides of the pan.
Let the cake cool in the pan for 10 minutes, and then transfer to a rack to cool completely.