Preheat the oven to 350°.
In a frying pan, brown butter over medium heat, stirring constantly until butter turns an amber color. Remove from heat as soon as the butter starts to brown.
Pour browned butter into a medium bowl and set aside to cool for 10-15 minutes.
Add brown sugar and sugar into the brown butter. Stir until combined. Using an electric mixer, beat the egg, egg yolk, vanilla, and sour cream to the brown butter mixture until combined.
In a medium bowl, whisk flour, baking soda and salt together. Gradually add dry ingredients into wet ingredients and beat on low speed until combined.
Stir white chocolate chips and peppermint chunks into cookie dough.
Wrap cookie dough in plastic wrap and place in the refrigerator for an hour.
Using a 1 inch cookie scoop, roll cookie dough into a ball, and place on ungreased baking sheet(s).
Bake for 10-11 minutes or until edges start to brown.
Remove from the oven, let sit on the cookie sheet for 5 minutes, then remove and place on a wire rack to cool.