Place the cold butter pieces into the bowl of a stand mixer fitted with the paddle attachment. Beat on medium speed for 5 to 7 minutes, scraping the bowl occasionally, until the butter becomes pale, light, and exceptionally fluffy.
Add 3 cups of powdered sugar and mix on low speed until fully incorporated. Pour in the vanilla extract and continue mixing for about 1 minute.
Add another 2 cups of powdered sugar and mix on low speed until combined. Increase the mixer speed to medium-high and whip the frosting for 3 minutes to create a light, airy consistency.
Continue adding the remaining powdered sugar 1 to 2 cups at a time, alternating with small amounts of heavy whipping cream. Mix on low speed after each addition, then increase to medium-high for a couple of minutes to develop a silky, spreadable frosting.
Add a pinch of salt to balance the sweetness. To eliminate excess air bubbles, reduce the mixer to its lowest speed and mix for about 1 minute. Finish by stirring the frosting gently with a spatula to achieve an ultra-smooth texture.
To Assemble the Cake
Once the cake layers have cooled completely, use a cake leveler or serrated knife to trim any domed tops, creating flat, even layers.
Spread a small amount of frosting onto your cake board or serving plate to anchor the cake. Position the first cake layer on top.
Fill a large piping bag fitted with a wide round piping tip—or simply trim the end of the bag—and pipe approximately 2 cups of frosting over the first cake layer. Begin around the outer edge and work toward the center before smoothing the frosting with an offset spatula.
Place the second cake layer on top and repeat the frosting process. Finish by adding the third cake layer.
Pipe frosting into any gaps between the layers, then apply a thin crumb coat over the top and sides of the cake. Smooth the frosting with an angled spatula or cake scraper, removing any excess while leaving a thin, even coating. Discard any crumb-coated frosting that contains cake crumbs rather than returning it to the mixing bowl.
Apply the final layer of buttercream over the entire cake using an offset spatula or a large piping bag fitted with a cake icing tip. Smooth the top and sides with an icing smoother until the finish is clean and even.
Decorate the cake with buttercream flowers and additional piping details as desired. Chill briefly before serving to help the frosting set and maintain crisp decorative edges.