Preheat the oven to 350°F (177°C) and place a rack in the center; line two standard cupcake pans with paper liners.
In a large bowl, sift together 2 1/4 cups cake flour, 2 teaspoons baking powder, and 1/2 teaspoon kosher salt; set aside.
In a measuring cup, whisk together 1 1/4 cups whole milk and 2 teaspoons vanilla extract; set aside.
In the bowl of a stand mixer fitted with the paddle (or using a hand mixer), beat 12 tablespoons unsalted butter and 1 1/2 cups sugar on medium speed for about 3 minutes, until very light and fluffy.
With the mixer on low, add one-third of the dry ingredients and mix until incorporated. Add half of the milk mixture and mix until combined. Add half of the remaining dry ingredients, then the rest of the milk, mixing until smooth. Finally add the last of the dry ingredients and mix until just combined.
In a separate bowl, beat the 4 large egg whites on medium-high speed until stiff peaks form.
Gently stir one-quarter of the whipped egg whites into the batter to lighten it, then carefully fold in the remaining whipped egg whites in two additions until no streaks remain.
Gently fold 1/2 cup sprinkles into the batter, being careful not to overmix to avoid bleeding color.
Using a large scoop or a 1/4-cup measure, divide the batter evenly among the 24 lined muffin wells, filling each about two-thirds full.
Bake for 18–24 minutes, or until a toothpick inserted in the center comes out clean. Transfer cupcakes to a wire rack and cool completely before frosting.