Grilled Turkey Cuban Sandwiches

Name: Grilled Turkey Cuban Sandwiches
Ingredients: 1 cup mayonnaise, divided; 1 tablespoon hot chili sauce (such as Sriracha); 1/3 cup (packed) finely chopped fresh mint; 2 tablespoons fresh lime juice; 2 tablespoons minced shallot; 1 teaspoon sugar; 1 teaspoon ground cumin; 1 1-pound loaf ciabatta bread, ends trimmed, bread cut crosswise into 6 pieces (each about 5x3 inches), each halved horizontally; 12 deli slices Swiss cheese; 1 pound thinly sliced Black Forest ham; 6 1/4-inch-thick slices cooked turkey breast; 6 tablespoons (about) butter