Preheat the oven to 350°F (175°C). Grease and lightly flour a 9x13-inch sheet cake pan or line with parchment.

In a large mixing bowl, whisk together the flour, granulated sugar, baking powder, and salt until evenly combined.

Add the 1 cup softened butter to the dry mix. Use a hand mixer or stand mixer on low to blend until the mixture looks crumbly and no large butter pieces remain.

Add the eggs one at a time, then the tablespoon of vanilla. Pour in the milk and increase speed to medium; mix just until the batter is smooth and homogenous.

Pour the batter into the prepared pan and spread it level with an offset spatula. Tap the pan lightly on the counter to release any large air bubbles.

Bake for 25-30 minutes, rotating the pan once halfway through if your oven bakes unevenly.

The cake is done when a toothpick inserted into the center comes out clean or with a few moist crumbs.

Let the cake cool in the pan for about 10 minutes, then transfer to a wire rack to cool completely before frosting.

For the frosting, beat the 1/2 cup softened butter until smooth and creamy.

Gradually add the powdered sugar, then the vanilla. Add heavy cream a tablespoon at a time until you reach a spreadable consistency.

Once the cake is completely cool, spread the buttercream evenly on top.