In a medium saucepan placed over medium heat, add the half-and-half and 1 ½ cups of the heavy cream. Add sugar and salt and whisk until dissolved. Stir in the mint leaves to steep.
While the cream mixture heats, add 2 egg yolks to the remaining ½ cup of heavy cream, whisking to combine. When the cream is hot, slowly ladle some of the hot cream into the cream and egg yolks, whisking continuously. This tempers the eggs.
Then slowly pour the egg yolk mixture into the hot cream mixture, while whisking. Cook over medium-low heat until slightly thickened, being careful not to boil the cream mixture.
Strain the mixture into a heat-proof bowl. Add green food coloring and whisk. Cover with plastic wrap, pressing the plastic wrap directly on top of the cream mixture. Refrigerate until completely chilled.
Meanwhile, place the Oreos in a zipper top bag and crush into pieces, Set aside.
Transfer the chilled cream mixture to an ice cream machine and churn until the mixture is the consistency of soft serve. When the ice cream is ready, transfer to a freezer-safe container. and fold in crushed mint Oreos. Freeze until firm, approx 3-4 hours.
Notes
To amplify the mint flavor, leave the fresh mint in the cream mixture while it chills. Strain out the mint leaves before adding cream to the ice cream machine.Yields 1 ½ quarts.