Preheat the oven to 350°F. Butter two 8-inch round cake pans, then cut out rounds of parchment to fit into the bottoms of the pans and insert them. Butter the parchment, and then flour the bottoms and sides of all of the pans.
In a large bowl (an upright mixer if you have one...otherwise use an electric mixer), beat the butter and sugar together until well combined. Beat in the eggs one at a time. Beat in the baking powder, salt and flour until combined, then beat in the milk and vanilla, mixing until the batter is smooth.
Divide the batter evenly between the two pans, and bake for 25 to 32 minutes, until a toothpick inserted into the center of the cakes comes out clean. Cool the cakes in their pans on wire racks for 15 minutes, then turn the cakes out of the pans, and finish cooling them upright on the wire racks.