Heat the oven to 325F. Line two cupcake pans with paper liners and set aside.
In a measuring cup, combine the egg, egg white, vanilla and oil. Whisk to combine.
In the bowl of a mixer fitted with the paddle attachment, combine the cake flour, sugar, baking powder and salt and mix on low speed for a minute to combine.
With the mixer still running, add in the softened butter pieces. Mix on low speed until the mixture resembles coarse crumbs. You should be able to gather a bit in your hand, squeeze and you have a solid piece. This means the butter is evenly distributed.
With the mixer still on low, slowly pour in the milk, mixing JUST until the flour mixture is moistened. You will not use all the milk at this time. Pour the remaining milk into the bowl with the eggs and oil, and whisk to combine. Set aside.
Turn the mixer speed to medium and whip for a full 90 seconds. The mixture should be whipped up, thick, and lighter in color.
Scrape the sides and bottom of the bowl to ensure everything is properly mixed.
With the mixer speed on low, add the egg/oil/remaining milk mixture in two additions, scraping down the bowl after each addition has been mixed in.
Once all the wet ingredients have been added, give the bowl a final scrape and mix with a spatula.
Fold in the sprinkles. Evenly divide the batter among the cupcake liners, 2/3 full.
Bake the cupcakes for 18-22 minutes, until a toothpick comes out with a crumb or two when inserted in the center of the cupcake. Don't over bake.
Place the baked cupcakes on wire racks to cool for 2 minutes. Carefully remove the hot cupcakes from the pan and cool completely on a wire rack.