In a large bowl, whisk together the flour, baking soda, and salt. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment (or using a handheld mixer), beat the butter on medium-high speed until smooth, about 1 minute.
Add the brown sugar and granulated sugar and mix on medium-high speed until light and fluffy, about 2 minutes.
Add the eggs and vanilla extract and beat until fully combined, scraping down the sides of the bowl as needed.
Gradually add the flour mixture to the butter mixture and mix on low speed until just combined.
Gently fold in 1 ½ cups of the red, white, and blue M&M’s by hand (or mix on low for just a few seconds).
Cover the bowl and chill the dough in the refrigerator for at least 2 hours (or up to overnight).
When ready to bake, preheat the oven to 350°F. Line baking sheets with parchment paper. Allow the dough to sit at room temperature for 10 to 15 minutes to make scooping easier.
Scoop 2 to 3 tablespoon portions of dough and place them on the prepared baking sheets about 2 inches apart. Press a few extra M&M’s on top of each cookie for a pretty, colorful look.
Bake for 11 to 13 minutes, until the edges are lightly golden and the centers still look slightly soft.
Remove from the oven and let the cookies cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.