Preheat the oven to 350 F. In a medium bowl, whisk together flour, oats, salt, and baking soda. In a large bowl, mix together butter, peanut butter, granulated sugar, and brown sugar until fluffy.
Add in the egg and vanilla extract and mix until it is fully combined. Add in the flour mixture until it is fully combined. Fold in the chocolate chips and M&Ms. Press the cookie dough into a greased round 9-inch cake pan.
Bake for 20-25 minutes. Let cool completely. In a large bowl, combine butter, peanut butter, powdered sugar, and vanilla extract until smooth. Pipe frosting onto cake.