Preheat the oven to 350°F (175°C). Grease and flour two 8-inch round cake pans or line with parchment paper.
In a medium bowl whisk together the all-purpose flour, baking powder and salt until evenly combined.
In a large bowl or stand mixer, cream the softened butter and granulated sugar on medium speed until light and fluffy, about 3 to 4 minutes. Add eggs one at a time, beating well after each addition, then mix in the vanilla extract.
With the mixer on low speed, add the dry ingredients in three additions alternating with the milk in two additions, beginning and ending with the dry ingredients. Mix until just combined; do not overmix.
Divide the batter evenly between the prepared pans and smooth the tops. Bake in the preheated oven for 25 to 30 minutes, or until a toothpick inserted into the center comes out clean.
Allow cakes to cool in the pans for 10 minutes, then turn out onto a wire rack to cool completely before frosting or serving.
Notes
Store cake layers wrapped in plastic wrap at room temperature for up to 2 days or refrigerate up to 4 days. Bring to room temperature before serving.