Preheat oven to 350°F/180 °C. Butter three 9-inch cake pans that are at least 2-inch high, and line the bottoms with parchment paper.
In a medium bowl, sift together flour, baking powder, baking soda, and salt. Set aside.
In the bowl of an electric mixer fitted with the paddle attachment, beat butter and sugar on medium speed until light and fluffy, 3-4 minutes. Scrape down the sides and bottom of the bowl as needed. Add eggs, one at a time, beating well after each addition. Beat in vanilla extract. With the mixer on low speed, add the flour mixture in three additions alternating with the buttermilk in two additions, beginning and ending with the flour mixture. Do not overmix this batter. The less you mix, the lighter the cake will be. Fold in sprinkles.
Frosting: In the bowl of an electric mixer fitted with the paddle attachment, beat butter and salt on medium speed until smooth and creamy, about 2 minutes. Add 5 cups powdered sugar, heavy cream, and vanilla. Beat on low speed for 30 seconds, then increase speed to high and beat for 2 minutes. Beat in more powdered sugar if frosting is too thin.
Frosting can be made 3 days ahead of time and kept in the fridge, covered. Cakes (unfrosted) can be made a day ahead and kept in the fridge, covered. The next day, bring frosting to room temperature and frost the cake. Frosted cake can be kept tightly covered in the fridge for 3-4 days. Leftovers can be kept in the freezer for up to 2 months and thawed overnight in the fridge.