In a mixing bowl with an electric hand mixer or bowl of a stand mixer fitted with a paddle attachment, cream together butter and sugars on medium speed until light and fluffy.
Add in eggs and vanilla extract and continue to mix until well combined.
Add in all-purpose flour, cocoa powder, baking soda, and salt. Mix until the dry ingredients are fully incorporated.
Fold in the semisweet chocolate chips and M&M candies until well dispersed throughout the cookie dough.
Portion the cookie dough into balls using a medium cookie scoop. Chill the cookie dough balls for at least 30 minutes.
Preheat oven to 350° F. Line a baking sheet pan with a silicone baking mat or parchment paper.
Place the cookie dough balls onto your prepared baking pans. Be sure there is space between the cookie dough balls to allow for spreading.
Bake for approximately 10 minutes. Cookies will appear underdone.
Remove from the oven. If desired, immediately press additional M&Ms into the warm, soft cookies. Allow the cookies to cool on the baking pan for 2 minutes before transferring to a wire rack to cool completely.