Before you start to mix this up, be sure you pre-freeze the ice cream canister that goes with your ice cream maker; if you don't, your ice cream won't freeze.
In a large mixing bowl, combine the whole milk, sugar, and salt 'til the sugar dissolves, about 1-2 minutes.
Whisk in the heavy cream, vanilla extract, peppermint extract, and green food coloring, if desired.
Turn on the ice cream freezer, and pour the mixture into the freezer bowl with the churn paddle in place.
Then place the cover on top, and let it mix 'til it thickens, about 20-25 minutes.
About 5 minutes before the freezing is completed (the ice cream should have a soft, creamy texture at this point), add the crushed Oreo cookies through the top of the ice cream maker, and let the cookie crumbles mix in completely.
Once the cookies are all mixed in, turn off the machine, and scoop the soft-serve ice cream into bowls for serving; or if desired, scoop it into an airtight container, and place it in the freezer for 2-3 hours to firm up more. Then serve when ready.
Notes
*I recommend freezing the crushed Oreo cookies ahead of time, so they don't warm and melt the ice cream when you add them. You can also use gluten-free Oreo cookies.