Dough requires chilling, so don’t preheat oven yet.
Combine the cool butter and shortening in mixer. Beat until creamy.
Add both sugars and continue beating on high for two minutes, scraping bowl. Beat in the vanilla and egg. Continue beating for another minute or until fluffy.Stir together the flour, salt and baking soda.
Add this mixture to the sugar mixture and stir until mixed. Stir in the M&Ms and chocolate chips. Chill batter for about an hour.Preheat oven to 350 degrees F. Drop batter by rounded teaspoonfuls onto ungreased cookie sheets, spacing 3 inches apart and bake for 12-14 minutes.
Let cool on cookie sheets for about 2 minutes, then transfer to wire rack to cool.