Preheat the oven to 350. Add softened butter, oil, and brown sugar to a bowl. Mix for 2 minutes. Add egg and vanilla and mix again.
Add flour, cornstarch, baking soda, and salt. Mix until dough is just combined.
Scoop out about 1/2 cup of dough. Flatten it in your hand and add 3-4 M&M's, either red or blue, on the center of the dough. Close the dough around the M&M's and roll it into a smooth ball. Place the dough ball on a lined or greased baking sheet and slightly flatten it with the palm of your hand.
Bake for 10 minutes. The cookies will look slightly undercooked, but they will set up. Remove from the oven and let the cookies set up on the pan.
While the cookies cool, make the frosting. Add the butter to a bowl and whip for 2 minutes. Add powdered sugar and vanilla and mix again. Add milk and mix again.
Add about 2 tbsp of frosting into 4 bowls. Add a couple drops of food coloring to each bowl, a different color in each bowl.
Add the frosting from each bowl into separate piping bags or ziploc bags. If using a ziploc bag, cut a small hole in the corner. Pipe the following shapes in the following colors, one shape per cookie. - yellow: star- red: triangle- blue: umbrella- green: circle Enjoy!