Preheat oven to 350℉. Grease and line the bottom of a small loaf pan with parchment.
In a small bowl, whisk together first four cake ingredients together. In a medium bowl, whisk together butter and sugar until well combined. Whisk in the egg, vanilla, and oil. Gradually stir dry ingredients into the wet until combined. Add milk and gently fold in sprinkles, if using them.
Pour batter into prepared pan. Cut a piece of rag long enough so it can wrap all the way around your loaf pan. Gently dampen the rag with cold water, and tie cake strip around pan (this will help the cake bake and cool flat, so you don't have to waste any of the cake to level the layers). Bake for 12-18 minutes, until a toothpick inserted into the center comes out clean. Let cool in the pan for a few minutes, and gently turn out onto a cooling rack.
To make the frosting, use an electric mixer to beat together frosting ingredients until creamy. Assemble however your heart desires - cut into equal squares and layer, use a round cookie cutter to make circular layers, or just ice as is and enjoy.