Coat a 9-inch pie pan with 2 teaspoons of the butter. In a food processor, chop the chocolate cookies into fine crumbs. Transfer to a small bowl and mix in the rest of the melted butter. Pat the mixture over the bottom and sides of the pan. Chill for at least 30 minutes.
Set a rack in the middle of the oven and preheat to 350 degrees. Bake the pie crust for 8 to 10 minutes, until set and dry. Place on a rack to cool.
For the Grasshopper Filling: Finely chop the white chocolate and put it in a medium bowl. In a small saucepan, over medium heat, bring 1/2 cup of the cream just to a simmer. Pour it over the chocolate and stir with a whisk until smooth and blended. Stir in the remaining 1/2 cup of cream and refrigerate for 30 minutes, until completely chilled. Whip to soft peaks, about 2 minutes, and place in the refrigerator until ready to use. In a small bowl, soften the gelatin by stirring in into the milk. Set aside.
Combine the yolks, eggs, and sugar in a medium bowl or double boiler and place it over a pan of slowly boiling water. Whisk until very hot to the touch but not scrambled (160 degrees). Remove the bowl from the heat and continue to whisk (you may switch to an electric mixer) until mixture is thick, double in volume, and, when tipped from a spoon, holds a ribbon shape for 2 seconds, about 2 minutes. Whisk in the creme de menthe and/or peppermint extract, if using.
Set the bowl of the gelatin over the pan of simmering water until gelatin has dissolved, about 1 minute, then whisk it into the egg mixture. Set aside to cool down to tepid. Whip the white chocolate cream until just thickened, then fold it into the egg mixture. Scrape the filling into the pie shell and refrigerate until set, at least 2 hours or overnight.