Preheat the oven to 350 degrees Fahrenheit. Line at least 2 cookie sheets with parchment paper, and set them aside.
Add the flour, baking powder, and salt to a large bowl and stir them together. Set the bowl aside.
Add the butter and sugar to the bowl of a stand mixer with the paddle attachment, and cream them together for about 3 minutes, until light and fluffy. (If you don't have a stand mixer, use a hand mixer).
Add the egg whites into the bowl in 3 batches. Mixing fully before adding in more eggs.
Add in the cake batter extract and vanilla extract and stir them in until combined.
Slowly add in the flour, a little at a time, mixing it completely before adding in more flour. Scrape down the sides of the bowl as needed.
Add the sprinkles to the batter, and fold them into the batter.
Separate the cookie dough into 12 even sized portions. Roll them into smooth balls, and place them onto the prepared cookie sheets, at least 6 inches apart.
Gently press the cookie dough balls down to flatten them into large circles.
Bake the cookies for 12-15 minutes, until the edges are lightly golden brown and the top center of the cookies looks dry and set.
Let the cookies cool completely on the cookie sheet, or after 10 minutes carefully transfer them to a cooling rack.