In a large bowl, whisk together the eggs, vegetable oil and the green food coloring.
Stir in the cake mix until combined then fold in 3/4 cup M&Ms.
Cover the bowl with plastic wrap and refrigerate the dough for 30 minutes.
Preheat the oven to 350°F. Line two baking sheets with parchment paper.
Remove the dough from the fridge and using an ice cream scoop (or two spoons) portion out about 2 tablespoons of the dough into mounds on the baking sheets, spacing the mounds at least 2 inches apart.
Bake the cookies until they are just set in the center, 12 to 15 minutes.
Remove the cookies from the oven and immediately press the remaining 1/4 cup M&Ms into the tops of the cookies. Let them cool on the baking sheet for 10 minutes then transfer them to a rack to cool completely.