Place sugars, eggs, butter, and peppermint extract in bowl of stand mixer. Mix on med-high speed until light and fluffy, about 4-5 min. Add eggs in one at a time, mixing just until incorporated.
In separate bowl, combine dry ingredients: flour, baking soda, baking powder, corn starch, cocoa powder, and salt. Whisk to combine well.
Fold dry ingredients into wet batter. Gently add in mint chips and semi-sweet chocolate chips. Form into dough ball, cover, and chill for 30 minutes or more.
Preheat oven to 350F, with rack on lower middle position.
Form 1.5 tablespoon-sized dough balls and place 2 inches apart on parchment-lined baking sheet. Bake 10-11 minutes*. Cookies may seem underdone, but will set nicely upon cooling.
Dough can be made up to a week ahead of time, wrapped, and chilled until ready to bake; be sure to give it a bit of time to sit at room temperature so it will be easier to form dough balls.
Bake 10 minutes for a slightly chewier/softer cookie. Bake 11 minutes for slightly crisper edges. Actual bake time will vary, depending on oven.
Baked cookies will keep nicely in an airtight container at moderate room temperature for several days. They can be frozen for up to a month.
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