Preheat oven to 350°F. Grease two 8-inch and two 6-inch round pans, line with parchment. Whisk flour, baking powder, baking soda, and salt. In a stand mixer, beat butter and sugar until light and fluffy, about 3 minutes. Beat in eggs one at a time, then vanilla. Alternately add flour mixture and buttermilk, mixing just until combined.

Divide batter among pans. Bake 8-inch layers 28-32 minutes and 6-inch layers 22-26 minutes, until a toothpick has moist crumbs. Cool 10 minutes in pans, then invert onto racks to cool completely.

For buttercream, beat butter and salt until creamy. Gradually add powdered sugar, beat on medium 3 minutes. Add vanilla and 3 tablespoons cream, beat until spreadable but stiff, adding more cream if needed.

Level cake layers if domed. Place one 8-inch layer on board, spread 1 cup buttercream, top with second 8-inch layer. Repeat with 6-inch layers, using 3/4 cup buttercream.

Stack the 6-inch tier (on its own board) onto the center of the 8-inch tier, securing with a bit of buttercream. Chill 15 minutes if wobbly.

Apply a thin crumb coat to the whole cake, chill 20 minutes. Frost with remaining buttercream, smooth, and decorate with sprinkles. Let stand at room temp 1 hour before serving.