In a small pot, simmer cream, milk, sugar, salt, creme de cacao and creme de menthe until sugar is dissolved, about 5 minutes. Remove pot from heat.
In a separate bowl, whisk yolks and mint extract. Whisking constantly, slowly whisk 1/3 of the hot cream into the yolks, then, whisk the yolk mixture back into the pot with the cream. Add green food colouring and mix to combine.
Return pot to medium-low heat and cook until mixture is thick enough to coat the back of a spoon. Pour into a freezer safe container.
Cool mixture at room temperature. Cover with plastic wrap and chill for at least 4 hours or overnight.
Churn cooled base in an ice cream machine according to manufacturer's directions.
Scoop chilled ice cream into a large mixing bowl and add chopped oreo cookies and mini marshmallows. Use a wooden spoon or spatula to incorporate into the mint ice cream base.
Serve Grasshopper Pie Ice Cream directly from the bowl as soft serve, or store in the freezer until ready to eat.