Prepare the Cake Layers
Preheat your oven to 350°F (175°C). Grease and line three 8-inch or 9-inch round cake pans with parchment paper. In a large mixing bowl, whisk together the flour, baking powder, baking soda, and salt. Set aside.
Cream Butter and Sugar
In a separate bowl, beat the butter and sugar with an electric mixer on medium speed until light and fluffy, about 3-4 minutes. Add the eggs, one at a time, beating well after each addition. Stir in the vanilla extract.
Combine Wet and Dry Ingredients
Add half of the dry ingredients to the butter mixture, followed by half of the milk, and mix on low speed. Add the remaining dry ingredients and milk, mixing just until combined. Do not overmix.
Bake the Cake Layers
Divide the batter evenly among the prepared pans, smoothing the tops. Bake for 25-30 minutes or until a toothpick inserted in the center comes out clean. Cool the cakes in their pans for 10 minutes, then transfer to wire racks to cool completely.
Prepare the Buttercream Frosting
In a large mixing bowl, beat the softened butter until creamy. Gradually add the powdered sugar, mixing on low speed until incorporated. Add the heavy cream and vanilla, and beat on high speed for 3-4 minutes until the frosting is light and fluffy. If desired, tint portions of the frosting with food coloring to match your baby shower theme.
Assemble the Cake
Place the first cake layer on a cake stand or serving platter. Spread an even layer of buttercream on top, then add the second layer, repeating with frosting. Place the third layer on top, applying a crumb coat (a thin layer of frosting) over the entire cake to seal in crumbs. Chill for 20 minutes, then apply a final layer of frosting, smoothing with an offset spatula.
Decorate
Use a piping bag to create borders, rosettes, or other designs with colored frosting. Add fondant decorations, edible pearls, or flowers for an elegant touch.