Crush the cookies into fine crumbs. You can do this in a food processor or by placing the cookies in a gallon-size ziplock bag and crushing them with a rolling pin (a good job for kids!). If you crush the cookies in the bag, you'll need to scrape the crumbs from the inside.
In a large bowl, mix the crumbs and the melted butter. Reserve 1 tablespoon of the mixture, then press the rest into the bottom and up the sides of a 9-inch freezer-safe pie plate. Set it aside.
Place the marshmallows and the milk in the top of a double boiler. (If you don't have a double boiler, place them in a bowl, then set the bowl over a pan of simmering water. Do not let the bottom of the bowl touch the water.) Melt the marshmallows over medium heat, stirring frequently, about 12 minutes. Remove the top bowl from the double boiler and chill it in the refrigerator for 10 minutes. Add the mint and coconut extracts and the food coloring, stir, and return the mixture to the refrigerator for 10 to 15 minutes.
Fold the whipped cream into the marshmallow mixture, then pour it into the pie shell. Sprinkle the reserved crumbs over the top. Freeze the pie for at least 2 hours. Remove the pie from the freezer 15 minutes before serving.