Adjust oven racks to the center. Preheat oven to 350 degrees F.
Grease (or line with parchment paper and grease parchment) three 8-inch round cake pans or one 8 x 12 oblong pan or one standard bundt pan.
Sift together the flour, baking powder and salt in a bowl, then whisk the mixture by hand to ensure that the ingredients are well mixed.
In a bowl, using a stand or hand mixer, add the butter chopped into large chunks. On a low speed, beat the butter until the texture is smooth and creamy (this should take about 30 seconds). Turn the mixer off and scrape down the sides of the bowl. Next, turn the mixer back on at medium speed and add in sugar gradually. Let the butter and sugar be whipped together for a couple of minutes until the butter and sugar are well blended and creamy. Turn off the mixer and scrape down the sides again.
Turn the mixer back on at low speed and slowly pour in vanilla extract and oil, alternating the two until well combined. Next, Add in egg and egg yolk one at a time and mix until batter is fluffy. Once all the eggs are added, turn off the mixer again and scrape down the sides of the bowl.
Turn on the mixer at medium speed, and alternate adding the flour mixture and milk. Continue to let the mixer beat everything together until the batter is well blended.
Spread batter evenly in cake pan, then tap pan on counter several times to eliminate air bubbles. Bake cakes until golden for about 35 to 40 minutes.
Remove the cakes from the oven and let cool in the cake pans on a wire rack.
Once the cakes are cooled, take the first baking pan and place your hand on top, then flip the pan upside down and gently slide the first cake layer on a plate or cake stand. You are now ready to cover the 1st layer with frosting (see buttercream frosting recipe below).
After each layer is frosted, repeat this step to carefully remove each cake layer from the pan and gently place on top of the frosted layer. Continue to frost each layer until covered, then use the remaining frosting to frost the sides of the cake.
Top the frosted cake with desired garnishments such as chocolate shavings or sprinkles.
Add cocoa powder to a large bowl and whisk until all lumps are removed.
Cream together the butter, vanilla extract, and cocoa powder until smooth.
Alternating between the milk and powdered sugar, slowly add to mixture.
Optional additions (sea salt, coffee, or cinnamon)
The frosting can be immediately applied to a cooled cake.
Homemade Yellow Birthday Cake Recipe: https://whatscookingamerica.net/cake/how-to-bake-a-cake.htm