Note: this dough requires chilling!
Pour butter into an electric mixer fitted with paddle attachment. While still hot, add both sugars and mix on low until combined. Let sit to cool for a few minutes.
While butter mixture is cooling, combine flour, baking soda, and salt in a medium bowl. Stir and set aside.
Turn mixer (with butter mixture bowl attached) on low. Add eggs, one at a time, mixing completely. Mix in vanilla extract. Add flour mixture to the wet ingredients and mix until combined. Stir in chocolate chips and mint chip pieces.
Scoop one tablespoon (or two tablespoon) balls of dough and place close together on a cookie sheet lined with parchment paper or a silpat baking mat. (If the dough is too soft to scoop, you can chill it for 30 minutes first.) Cover the cookie dough balls with plastic wrap and chill overnight.
Preheat oven to 350°F. Line cookie sheets with parchment or silpat liners. Place cold cookie dough balls 2 inches apart.
Bake for about 10-12 minutes. They will be golden on the outside and still doughy on the inside. I like my cookies a little underdone, so I bake them for 10 minutes, but if you like a more done cookie, do 12 minutes. Let cool for 5 minutes, and then remove from pans to cool completely.