Preheat the oven: Set your oven to 350°F (175°C). Grease and flour two 9-inch round cake pans, or line with parchment paper.
Prepare the dry ingredients: In a medium bowl, sift together the flour, baking powder, and salt. Set aside.
Cream the butter and sugar: In a large mixing bowl, beat the butter and sugar together until light and fluffy, about 3-4 minutes.
Add the eggs: Add the eggs one at a time, beating well after each addition. Stir in the vanilla extract.
Combine wet and dry ingredients: Gradually add the dry ingredients to the wet ingredients in thirds, alternating with milk. Mix until just combined. Be careful not to overmix.
Bake the cake layers: Pour the batter evenly into the prepared cake pans. Bake for 25-30 minutes, or until a toothpick inserted into the center comes out clean.
Cool the cakes: Allow the cakes to cool in the pans for 10 minutes before transferring to a wire rack to cool completely.
Frost the cake: Once the cakes have cooled, spread a thin layer of buttercream frosting over one layer of the cake. Place the second layer on top, and apply a crumb coat. Chill for 30 minutes, then apply a final layer of frosting.
Decorate: Add baby-themed decorations, fresh flowers, or sprinkles to finish. Serve and enjoy!