Grease a 9 x 5-inch loaf pan lightly. Line the bottom and short sides with parchment paper, letting the ends extend over the sides for easier removal after baking.
In a medium bowl, combine the flours, baking powder, and salt. Set this mixture aside.
In a stand mixer equipped with the paddle attachment, cream the butter and sugar on medium speed until the mixture is light and fluffy, which should take about 4 minutes.
Add the eggs and egg yolks one at a time, ensuring each one is fully mixed in before adding the next. Scrape down the sides of the bowl as needed.
Mix in the vanilla extract until everything is well combined.
Beat the mixture on medium speed until it is light and fluffy.
Gradually add the flour mixture to the egg mixture, alternating with the milk and yogurt, beginning and ending with the flour mixture.
Once the batter is well combined, remove the bowl from the stand mixer and fold in the rainbow sprinkles with a spatula or wooden spoon.
Transfer the batter to the prepared loaf pan, smoothing the top gently with an offset spatula.
Bake for 60-65 minutes, checking the cake at the 50-minute mark. If the top is browning too quickly, cover it loosely with aluminum foil.
The cake is done when it springs back upon gently pressing the top and a toothpick inserted into the center comes out clean.
Take the cake out of the oven and let it cool in the pan for 10 minutes.
Using the parchment paper ends, lift the loaf out of the pan and place it on a cooling rack to cool completely.