Preheat oven to 350°F (175°C). Grease and flour a 9-inch round cake pan.
In a large bowl, combine flour, sugar, baking powder, and salt.
Add butter and milk to the dry ingredients and mix until just combined.
Beat in eggs one at a time, then stir in vanilla extract.
Pour batter into the prepared pan and bake for 30-35 minutes, or until a toothpick inserted into the center comes out clean.
Let the cake cool in the pan for 10 minutes before inverting it onto a wire rack to cool completely.
While the cake is cooling, prepare the frosting. In a large bowl, beat butter until creamy. Gradually add powdered sugar, alternating with milk, until smooth and fluffy. Stir in vanilla extract.
Frost the cooled cake and enjoy!
Notes
For a richer flavor, you can use brown butter instead of regular butter.