Preheat oven to 350 degrees F. Line cookie sheet with parchment paper or silicone baking mat.
In the bowl of a stand mixer using the paddle attachment, cream the butter and sugar together on medium speed until light and fluffy, about 3 minutes. Add the egg yolks, vanilla extract, and peppermint extract and beat until well combined for about a minute, scraping sides as needed. In a separate bowl, combine flour, baking powder, and salt. Mix into butter mixture until a dough forms. You may need to do the final mixing by hand as the dough will be thick. Fold red sugar into dough.
Roll dough into teaspoon sized balls and set about 2 inches a part on prepared baking sheet. Bake in preheated oven for 9-10 minutes and remove when set but not yet turning brown. Wait 2-3 minutes so that cookies have cooled a bit but are still warm and gently press a peppermint kiss into the top of each cookie. If you do this too soon, it may melt. If you wait too long, they may not stick to the cookie. Transfer to wire cooling rack.