Mix the milk, cream, peppermint extract and green food coloring together in a large liquid measuring cup and refrigerate until cold. Turn your ice cream machine on and pour in the cream mixture. Churn until the mixture looks slushy like soft serve, about 12 to 15 minutes. Stir in the chocolate morsels.
Transfer the ice cream to another container and put plastic wrap on top of the ice cream. Cover the container tightly with a lid. Freeze for several hours until firm enough to scoop.
To assemble sundaes, scoop ice cream into 4 bowls. Top with hot fudge sauce, whipped cream, and chocolate shavings. Top with a cookie and serve.
Melt the chocolate and butter in a small glass bowl over a pot of simmering water. Whisk together until smooth and glossy. Remove from the heat and whisk in corn syrup and vanilla extract until smooth.
Dip the cooled cookies into the glaze and remove, with a fork, to a wire rack set over a sheet tray. Allow the cookies to set for 40 minutes before serving.
Whisk together flour, cocoa powder, espresso powder, baking powder, and salt in a small bowl.
In a large bowl, add the butter and sugar and cream together, using an electric mixer, until light and fluffy. Beat in the eggs and vanilla, then slowly add the dry ingredients. Form the dough into a long 2-inch thick log on parchment paper and roll tightly. Freeze for at least 4 hours to overnight.
Arrange racks in the middle of the oven. Preheat the oven to 375 degrees F.
Slice the dough into 1/4-inch rounds and arrange them on a parchment lined baking sheet, about 1-inch apart. Bake for 12 to 15 minutes. Remove and let cool for 5 minutes on the baking sheet, then remove to a wire rack. Let cool completely before glazing.
Make sure that your ingredients are all well chilled before you add them to your ice cream maker. Add the chocolate chips after the mixture has partially frozen. If you don't wait, the chips will all settle to the bottom of the ice cream and freeze there.