With a mixer or a wooden spoon, cream together the butter and peanut butter. Add in the brown sugar, granulated sugar, vanilla, and eggs. Mix until the batter is smooth and silky looking.
Mix in the baking soda, cornstarch, and oatmeal. Add in the flour and mix well.
Lastly, by hand mix in the M&M candies and chocolate chips.
Place the dough in the fridge to chill while preheating the oven to 350 degrees. If using a baking stone, place it in the oven as it preheats.
Using a medium cookie dough scoop, drop the cookies a couple inches apart onto the baking stone or cookie sheet. Do not press flat. They will flatten out somewhat as they bake.
Bake for 10-11 minutes or until slightly golden brown around the edges.
Immediately remove from the baking stone or cookie sheet to cool.
Store in an airtight container. They freeze well too.