In a medium bowl or liquid measuring cup, combine the buttermilk, vanilla extract, and vegetable oil. Set aside.
In a large bowl, whisk together the flour, baking powder, salt, and baking soda. Set aside.
In a separate large bowl, combine the granulated sugar, light brown sugar, and butter. Beat with an electric hand mixer on high speed until super light and fluffy, about 4 minutes.
Add the eggs and egg yolks one at a time, beating in between additions. Beat the batter until almost doubled in volume and very light and fluffy, about 5 minutes.
With the mixer on low, gently beat in a third of the flour mixture. Before it's fully combined, add half of the buttermilk mixture. Repeat with remaining flour and buttermilk until everything is well-blended and no lumps remain.
Preheat the oven to 350°F (180°C). Spray 3 9-inch (23 cm) round cake pans with nonstick spray.
Add ½ cup (80 g) of sprinkles and gently fold into the batter with a spatula until well-incorporated.
Divide the cake batter among the prepared pans and place 2 pans on the top oven rack and 1 pan on the middle rack.
Bake for 30 minutes, rotating the pan on the middle rack to the top rack, and vice versa, halfway through baking, so the cakes bake evenly. The cakes are done when they are golden brown, pull away from the sides of the pans, and the tops spring back slightly when pressed.
Remove the cakes from the oven and invert them onto a wire rack to cool completely. (If you don't have a wire rack, let them cool in the cake pans on the counter.)
Make the frosting: In a large bowl, use an electric hand mixer on high speed to beat the butter, cream cheese, and salt. Mix until light and creamy, about 4 minutes.
Add the powdered sugar and beat on low speed to combine. Once the sugar is incorporated, beat on high speed until there are no lumps and the frosting is super white and fluffy, about 5 minutes.
Place a dab of frosting on a cake stand or an inverted plate. Place a layer of cake on the cake wheel, then evenly spread frosting on top with an offset spatula. Place the next layer of cake on top of the frosted layer, and spread frosting on top. Add the last cake layer and lightly frost the entire outside of the cake to create a thin crumb coat.
Chill the cake in the refrigerator for 20 minutes.
Remove the cake from the refrigerator and use the remaining icing to frost the cake in an even layer. Take the end of an offset spatula or knife and gently press it against the against the frosting at the bottom of the cake. Then, spin the cake and slowly raise the spatula after each rotation to create a ribbed effect. Smooth the top of the cake with the spatula.
Place sprinkles around the edge of the cake. Set a small cookie cutter, any shape you like, in the center of the cake and fill in with sprinkles. Gently remove the cookie cutter.