Place the heavy cream and milk together in a saucepan set over medium high heat, and heat it up until you see bubbles around the edge (you’re scalding the mixture). Be careful not to let it boil. Remove the mixture from the heat.
Whisk together the egg yolks and sugar until the mixture gets thick and light yellow in color. Slowly add in the cream mixture while constantly whisking, then return all of the liquid to the saucepan, and cook over medium heat until the mixture thickens slightly and coats the back of a wooden spoon (if you have a thermometer, heat it to 165). Add the peppermint extract to the mixture.
Strain the mixture, then cool it completely either by placing it in the fridge, or for a speedy method, placing it in a bowl set in an ice bath. When completely cold, pour the mixture into your ice cream maker along with the chocolate chips, and spin until frozen.
Place the mixture into a container and freeze completely.
To assemble the sandwiches, place a scoop of gelato between the two cookies and press together to form a sandwich. Enjoy!