Preheat the oven to 350 degrees F. Line a cupcake tin with cupcake liners.
In a small bowl, whisk together the flour, baking powder and salt.
In a larger bowl, use an electric mixer to combine the butter; beat until creamy. Add the sugar and mix on high speed until fluffy, 1 to 2 minutes. Add the egg and egg white, mixing well on medium speed until combined. Scrape down the sides of the bowl if needed. Beat in the oil and vanilla.
With the mixer on low speed, mix in half of the dry ingredients. Mix in the milk. Then mix in the rest of the dry ingredients and beat until well combined. Use a rubber spatula to gently stir in the sprinkles.
Fill the cupcake liners ⅔ full. Bake until the tops are set, 18 to 20 minutes. Let cool completely before frosting.
FROSTING
In a large bowl, use an electric mixer to combine the butter and cream cheese on high speed until creamy and well combined.
With the mixer on low speed, slowly add the powdered sugar. Beat until the sugar is incorporated, and then add the vanilla. Scrape down the sides of the bowl, if needed. Beat the frosting on high speed for 1 to 2 minutes, until fluffy and creamy. If the frosting seems too thick, beat up to a tablespoon of milk until well combined.
Frost the cupcakes and top them with the sprinkles.
Notes
Because there is cream cheese in the frosting, I keep these in a covered tub and store them in the refrigerator until they are ready for munching.