Preheat oven to 350 degrees F.
In the bowl of a stand mixer, cream butter and sugars. Add vanilla and egg, mix until incorporated.
In a separate mixing bowl, sift flour, cornstarch, baking soda and salt. Mix in dry ingredients, one cup at a time, until smooth.
Add M&M’s or chocolate chips, gently fold in.
Place cookies on sheet using a standard scoop. Bake for 8-10 minutes or until edges are golden brown. (Since I made giant cookies I used 2 scoops of dough, patted them together, put 6 on a sheet, flattened them, and baked them for 14 minutes).
Remove from oven and let cool on sheet for 5 minutes before transferring to a wire rack to cool completely.
While cookies are cooling, prepare frosting by beating together butter, milk, salt and extracts until light and fluffy. With mixing speed on low, slowly add the powdered sugar. Beat for 2-3 minutes. Pipe (or spread) onto cookies & sandwich.