Cream the butter and sugar. In a large mixing bowl, beat ¾ cup softened butter, ¾ cup granulated sugar, and ¾ cup packed brown sugar on medium speed until smooth. Then, add the eggs and vanilla and continue beating for 3-5 minutes until the mixture is light and fluffy. Next, scrape down the sides of the bowl as needed to make sure it's even mixing.
Mix the dry ingredients: Whisk together 2¼ cups plus 2 tablespoons of all-purpose flour, 1 teaspoon baking soda, and ¾ teaspoon salt in a separate bowl. Slowly add the dry ingredients to the butter mixture, mixing at low speed, one cup at a time, until combined.
Add the M&Ms. Using a spatula or wooden spoon, fold in 1½ cups of Christmas M&Ms by hand until evenly distributed throughout the dough.
Chill the dough. Cover the mixing bowl with plastic wrap and chill the dough in the refrigerator for at least 1 hour. Chilling the dough helps the cookies keep their shape and enhances their flavor.
Preheat the oven and prepare the baking sheets. Toward the end of the chilling time, preheat your oven to 350°F (175°C) with the oven rack in the center. Then, line two baking sheets with parchment paper or lightly coat them with cooking spray.
Shape and top the cookies. Use a tablespoon or a small cookie scoop to portion the dough into balls, placing them about 2 inches apart on the prepared baking sheets. Press 2-3 additional M&Ms on each dough ball for a festive look.
Bake. Bake in the oven for 11-13 minutes or until the edges are lightly golden. The centers may still look soft with a chewy texture as they cool.
Cool. Let the cookies cool on the baking sheets for 5 minutes, then transfer them to a wire rack to cool completely.