Preheat the oven to 350°F. Butter and flour two mini cake pans (mine were 4 1/2 x 2 inches).

In a small bowl, whisk together 1 1/2 cups cake flour, 1 teaspoon baking powder, and 1/4 teaspoon salt. Set aside.

In the bowl of an electric mixer, add 1/2 cup unsalted butter (room temperature) and beat until creamy.

Add 1 cup granulated sugar and beat on high speed for 2 to 3 minutes, until the mixture is light and fluffy.

Add 1 large egg and 1 egg white and mix on medium speed until combined. Scrape down the sides of the bowl as needed.

Add 2 tablespoons vegetable oil and 3 teaspoons vanilla extract and beat on medium speed for about 1 minute.

With the mixer on low speed, add half of the dry ingredients. Pour in 1/2 cup whole milk. Add the remaining dry ingredients and mix on medium speed until just combined. Scrape down the bowl once more.

Use a large spatula to gently fold in 1/3 cup assorted brightly colored sprinkles, taking care not to overmix.

Divide the batter evenly between the two prepared pans and smooth the tops.

Bake for 18 to 20 minutes, or until the tops are set and a toothpick inserted in the center comes out with just a few moist crumbs.

Let the cakes cool in the pans for 5 to 10 minutes. Run a knife around the edges if needed, then turn the cakes out onto a piece of parchment paper and let them cool completely.

Once completely cool, use a 2-inch biscuit cutter to cut rounds from the cakes. (Reserve leftover cake pieces or crumbs for sprinkling if desired.)

To make the frosting: in the mixer bowl, beat 1/2 cup unsalted butter (room temperature) and 8 ounces cream cheese (room temperature) on high speed until smooth and combined.

With the mixer on low speed, slowly add 2 1/2 cups powdered sugar until incorporated. Add 1 tablespoon vanilla extract and scrape down the sides of the bowl.

Beat the frosting on high speed for 2 to 3 minutes until fluffy and creamy. If the frosting seems too thick, beat in up to 1 tablespoon whole milk for 1 to 2 minutes until spreadable.

Assemble the mini cakes: place a cake round on a plate, spread an even layer of frosting, top with another round if stacking, and frost the outside as desired.

Finish by pressing 1/4 cup assorted brightly colored sprinkles onto the tops and/or sides of the frosted mini cakes. Chill briefly to set the frosting if desired, then serve.