Bake the cake layers: Heat oven to 350°F (180°C). Butter and line three 6-inch cake pans with parchment paper and set aside.
In a large jug whisk together the egg whites, whole egg, milk, and vanilla extract. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment (or with a medium bowl and a handheld electric mixer), combine the Almond Flour Baking Mix, sugar, baking powder and salt together at low speed for 1 minute.
Add the cold butter and continue to mix on low until the mixture is a fine crumbly texture.
Turn the mixer up to medium speed and add the liquid mixture in 2 increments, making sure to scrape the sides and bottom before and after each batch, until fully blended.
Divide the batter evenly into the prepared pans and bake until a cake tester inserted in the center comes out clean or with a few crumbs attached, about 25-35 minutes.
Let the cakes cool in the pans for 20 minutes before removing them from the tins and transferring to wire racks to cool completely.
Assemble the Cake: If the cake layers are domed, use a serrated knife to cut flat, even tops.
Place the bottom cake layer on a serving plate or cake turntable.
Spread about ½ cup of buttercream frosting on top with a small offset spatula. Gently place the 2nd cake layer face down on top. Place another ½ cup of frosting on top of this layer and spread out.
Gently add the 3rd cake layer. Add on a generous scoop of frosting and spread evenly over the top and sides until you have a very thin layer of frosting over the entire cake. This is called the “crumb coat”. Chill until the frosting is set, about 30 minutes.
Remove from the refrigerator and apply a thick, final layer of frosting over the crumb coat. Decorate all over with sprinkles. Just keep on applying them until they stick all over.
Store at room temperature for up to 1 day. For longer storage, refrigerate, well covered, for up to 3 days. Before serving let it rest at room temperature for 30 minutes and then enjoy!