Preheat the oven to 425°F.
Place the cookies into the bowl of a food processor fitted with an S-blade, then drizzle in the melted vegan butter while the machine is running. Process the mixture to crumbs, stopping to scrape down the sides of the bowl as needed (Note 1).
Press the mixture into the bottom and up the sides of your pie plate. Press firmly, just until the crust feels stable. Don't pack the mixture or it will be difficult to remove from the plate when serving.
Bake the crust for about 8 minutes, until it looks slightly glossy. Transfer it to a cooling rack when done — it will firm up as it cools.
To make the filling, start by placing the coconut milk, creme de menthe, and creme de cacao into a small saucepan over medium heat. Bring the mixture to a low boil, then reduce the heat and let it simmer for 8 minutes.
Stir in the marshmallows, adding a few at a time if they won't all fit. Keep stirring the mixture over low heat until the marshmallows melt and the mixture is smooth. This can take a few minutes.
Remove the pot from heat. Let the mixture cool until it's just a bit warm, about 30 minutes. The mixture will thicken and congeal a bit as it cools, and this is fine. Give it a stir every few minutes to mitigate this, and avoid letting it cool completely or it can become too firm to work with.
Open the can of coconut cream, then transfer the solids only to a large mixing bowl. Discard any liquid in the can or save it for another use. You should end up with about 1 cup of coconut cream. Using an electric mixer on high speed, beat the coconut cream until fluffy, about 1 minute, then add the marshmallow mixture to the bowl and continue beating until fluffy and evenly mixed. Beat in the peppermint extract, along with the food coloring, if using.
Transfer the filling to the crust and smooth out the top with a spatula.
Freeze the pie until set, at least 4 hours. The filling will still be slightly soft when the pie is fully set.
Optionally, sprinkle the top of the pie with chocolate shavings and decorate with vegan whipped cream.
Slice and serve.