Low FODMAP Frozen Hot Chocolate

Name: Low FODMAP Frozen Hot Chocolate
Prep time: 15 min
Cook time: 5 min
Total time: 20 min
Cuisine: American
Ingredients: 3 tablespoons sugar, (divided); 2 teaspoons black cocoa; 2 teaspoons Dutch-processed cocoa; 2 teaspoons natural cocoa; 1 ½ cups (360 ml) cold lactose-free whole milk, (divided); 2- ounces (55 g) bittersweet chocolate, (finely chopped, preferably 65% to 80% cacao mass); 2- ounces (55 g) semisweet chocolate, (finely chopped, preferably 50% to 55% cacao mass); 2- ounces (55 g) milk chocolate, (finely chopped); 1- pound (455 g) ice cubes; about 4 cups of standard sized cubes; 1/2 cup (120 ml) chilled lactose-free heavy cream