Preheat the oven to 400 degrees. Line 2 baking sheets with parchment paper.
In your mixer bowl, cream together the cold, cubed butter or margarine and both sugars for approximately 3 minutes.
Beat in the eggs and the vanilla, one at a time, scraping down the sides in between.
In a separate bowl, whisk together the flour, pudding mix, baking soda and salt.
Add it to the creamed sugar mixture and stir until combined.
Mix in the white and semi-sweet chocolate chips, then stir in the M&M's.
Using a 2 Tbsp cookie scoop, scoop the dough on to your prepared trays, leaving about 2 inches between each cookie ball.
Press extra M&M's in to the top of each ball of dough if desired. I press in 3 different colors, just to help them show better in the cookies.
Bake for 8-9 minutes until the cookies are light golden brown on the top. (For best results I cook one tray at a time on the middle shelf.)
Remove from the oven and let the cookies sit on the trays on a cooling rack for 5 minutes, then transfer the cookies to the cooling racks.