Heat oven to 325°F. Break up cookie dough into the bowl of a stand mixer. Add scant 1/2 cup of flour and use the paddle attachment to mix it into the dough. (A hand mixer also works!)
Flatten dough into a disc and wrap in plastic wrap. Chill for 15 minutes. Cover 2 sheet pans with parchment paper.
Remove dough from refrigerator and roll out to about 1/8-inch thick on a floured surface. Cut out circles using a 2 3/4-inch cookie cutter. Combine scraps. Reroll dough and cut more rounds. Transfer to a baking sheet and bake for 12 to 15 minutes until done. Let cool.
Dye half the frosting green. Fill a piping bag, fitted with the #233 grass tip, with the green frosting. Fill a second piping bag, fitted with a #4 round tip, with the remaining white frosting.
Show the kids how to pipe green frosting “grass” on the round cookies, then use the white frosting to add yard lines and numbers.