Center a rack in the oven and preheat to 350 (F). Prepare two 8-inch cake pans by spraying liberally with cooking spray and lining the bottom of each pan with parchment paper circles. Lightly spray the parchment paper and set aside.
In a medium bowl, whisk together 2 1/2 cups cake flour, 2 1/4 teaspoons baking powder, 1 teaspoon vanilla bean powder, and 3/4 teaspoon kosher salt. Set aside.
In the bowl of a freestanding electric mixer fitted with a paddle attachment, combine 1 cup unsalted butter and 1 1/2 cups granulated sugar and cream on medium-high speed for at least 5 minutes, until light, fluffy and doubled in volume. Lower the mixer speed to its slowest setting and add 4 large egg whites, one at a time, only adding the next one until the previous egg white has been fully incorporated. In a small liquid measuring cup, whisk together 1/4 cup plus 2 tablespoons vegetable oil and 2 teaspoons Princess Bakery emulsion and slowly stream into the egg mixture until fully incorporated.
With the mixer running on low, add the flour mixture (from the 2nd step) to the butter mixture in three additions, alternating with adding 1 cup whole milk in two additions, starting and ending with the flour mixture. Mix on low speed until just incorporated — be careful not to overmix! It's okay to have one or two flour streaks left at this point.
When the dry ingredients have just about disappeared, stop the mixer. Use a rubber spatula to fold in 2/3 cup of sprinkles into the batter. Be careful not to overmix! Again, just fold until the sprinkles are evenly incorporated throughout the batter.
Divide the batter evenly between the prepared pans. Transfer the pans to the preheated oven and bake the cakes for 35 to 40 minutes, until a toothpick inserted into the center of the cake comes out clean and the tops of each cake bounce when gently poked with a finger.
When the cakes are finished, transfer the cakes to a wire rack. Allow to cool in pans for 15 minutes, before turning out of the pans to cool completely. Allow the cakes to cool completely before frosting.