In a small bowl, whisk together flour, baking soda, and salt. Set aside.
In a large bowl, beat together butter and shortening until well-combined.
Add sugars, and beat for about 4-5 minutes on high, or until very well-combined.
Add eggs, one at a time, and vanilla; beat in for 3 minutes.
Stir in flour until just combined.
Add chocolate chips and M&M's; stir in.
Cover, and refrigerate dough for at least 2 hours.
Preheat oven to 375 F, and line 2 baking sheets with parchment paper.
Drop dough by medium scoops (1.5 tablespoons) onto prepared cookie sheets.
Bake for about 8-10 minutes, or until very lightly browned at the edges.
Remove from oven, and let cool on baking sheet.
Notes
It's key to properly measure the flour. The most accurate way to measure the flour is to weigh it (click on "metric" immediately underneath the ingredients to get the weights). If you aren't weighing the flour, sift or stir it to break it up. Lightly spoon the flour into a measuring cup and level. Avoid packing the flour because it will give you dry, crumbly dough.
Please don't skip the chilling time. Otherwise, the cookies will bake out and be flat without it.
Using a cookie scoop will make it easier to portion the dough and will give you uniform cookies.
Slightly underbaking the cookies will help to keep the cookies soft and chewy.