Preheat the oven to 350 F. In a medium bowl, whisk together flour, oats, pudding mix, salt, and baking soda. In a large bowl, mix together butter, peanut butter, and both sugars until fluffy. Add in egg and vanilla extract until smooth.
Add in the flour mixture and mix until it is fully combined. Fold in the chocolate chips and M&Ms. Roll the cookie dough into balls and place one Oreo cookie in each cookie dough and roll into balls.
Place cookies onto a large ungreased baking sheet at least 2-inches apart. Bake for 10-12 minutes.