Mix the peanut butter and butter until smooth. Add the sugar and beat mixture until well combined. Add the egg and vanilla and mix until well combined.
Mix together the oats, flour, salt, soda, and cinnamon. Add to the wet ingredients and mix until combined. Stir oatmeal in the M&Ms.
Bake 1/4 cup scoops on ungreased baking sheets for about 13-14 minutes or until they look done. Allow cooling before filling.
Bring a shallow pot of water to a boil. Place all the ingredients for the filling in a bowl that can rest in the boiling pot without its bottom touching the boiling water. Beat the oatmeal ingredients until the bottom of the bowl is too hot to touch.
Remove the bowl and beat with the whisk attachment on your stand mixer for about 10 minutes or until fluffy and pretty stiff. You can also use a handheld mixer, but it will take longer.
Use filling to sandwich together with the cookies and decorate the edges with rainbow sprinkles.