In a heavy saucepan over medium-high heat, combine the sugar with 1/4 cup of water.
Bring to a simmer and cook until the mixture turns a deep golden brown. Remove from the heat and carefully whisk in the heavy cream, vanilla extract and salt. Set aside to cool to room temperature.
Combine the cookie crumbs and chocolate chunks in a large resealable bag.
Using a large round ice cream scoop, scoop out a ball of ice cream and leave it in the scoop. Poke a hole in the center of the scoop with a handle of a wooden spoon and put a cherry into the hole. Cover the hole with a bit of ice cream and put the scoop of ice cream into the bag of cookies and chocolate pieces. Shake around pressing gently to completely coat the ice cream. Put the scoop on a tray and freeze for 30 minutes. Repeat the process with remaining ingredients.
Before serving, divide the caramel sauce among 4 plates. Remove the Tartufos from the freezer and slice them in half. Arrange 2 halves on each plate and garnish with mint sprigs.