Limonana Sorbet

Name: Limonana Sorbet
Cook time: 8 h
Total time: 8 h
Cuisine: European, Mediterranean, Italian
Ingredients: 2/3 cup sugar; 1 and 2/3 cups water, divided; 1 cup + 1 tablespoon freshly squeezed lemon juice; 3/4 cup loosely packed mint leaves, plus more for garnishing; 1 teaspoon lemon zest, or to taste (do not omit); 1 cup ice cubes; hollowed-out lemon halves, for serving (optional)