In a heavy stainless steel saucepan, combine the sugar and water together. Add the mint. Bring the liquid to a boil. Reduce the heat to medium and simmer for a couple of minutes. Remove from the heat and cool completely. Strain the liquid through a fine mesh strainer, discarding the mint. Stir in the creme de menthe.
In a large nonstick saucepan, combine the cream and mint syrup. Bring the liquid to a gentle boil. In a mixing bowl, whisk the yolks together. Whisk 1 cup of the hot cream into the egg yolks. Slowly whisk the egg mixture back into the cream mixture. Whisk until smooth. Reduce the heat to medium-low and continue to cook for 4 minutes. Remove from the heat and cool completely. Strain the liquid and fold in the chocolate pieces. Add the liquid to the ice cream machine container and process according to manufactures directions. Place one large scoop in the center of six cookies and place the remaining cookies on top of the ice cream. Press the cookies together, forming the sandwiches. Serve the sandwiches with a drizzle of the chocolate sauce.