Preheat oven to 350°F. Line a 9” round cake pan with foil and spray with nonstick cooking spray.
Make the cookie cake: Beat butter and sugar with a hand or stand mixer until creamy. Beat in egg and vanilla, then mix in baking soda, salt, and cream of tartar. Slowly mix in flour. Stir in M&Ms and sprinkles.
Press batter into prepared pan, pressing more M&Ms onto the top as desired. Bake for 19-22 minutes or until the edges are just turning a light golden brown. It’s better to under bake this dough than over bake it. The cake will continue cooking a bit as it cools, so err on the side of underdone for the best tasting cookie. Let it cool completely before frosting.
Make the frosting: Beat butter until smooth, then slowly beat in powdered sugar until crumbly. Add salt and vanilla, then add 1 tablespoon of heavy whipping cream. Beat until smooth, adding more a teaspoon at a time to get a spreadable texture.
To frost: Use a 1M tip and a ziplock or piping bag to decorate the cookie cake. Top with more sprinkles and M&Ms.
Store loosely covered for up to 2 days.