In a medium bowl, whisk together flour, oats, salt and baking soda. In a large bowl using either a hand or stand mixer, beat softened butter with peanut butter and both sugars until fluffy.
Add in eggs and vanilla extract. Beat until smooth. In three separate additions, add flour mixture to butter mixture beating after each addition until fully incorporated.
Fold in m&ms and chocolate chips. Cover and refrigerate dough for at least one hour. Preheat oven to 350 F. Roll dough into balls and place 2-inches apart on ungreased baking sheets. Bake for 10-12 minutes.