Ensure the butter is at room temperature, then beat the butter and oil together for 3 minutes or until smooth and creamy. The mixture should be pale yellow without any butter chunks.
Slowly pour in granulated sugar while mixing on medium-high speed for about 3 minutes or until the mixture becomes fluffy and almost white.
Add room temperature eggs one by one, fully mixing each before adding the next. Add vanilla extract and beat for 3 more minutes until the batter turns pale yellow and bubbles appear on the surface.
Sift salt, baking powder, and cake flour together.
Alternate adding flour and buttermilk to the batter, ending with flour. Mix until just combined, then gently fold in the colorful sprinkles.
Bake these mini cupcakes until golden brown on top, and a toothpick put into the middle comes out quite clean (no coarse crumbs). Let them cool completely before frosting.