Marinate the Chicken a medium bowl or zip-top bag, dissolve the salt and sugar in cold water. Slice the chicken breasts in half horizontally, then submerge them in the brine. Cover or seal, and refrigerate for at least 30 minutes (up to 8 hours for deeper flavor and tenderness). After marinating, remove the chicken from the brine and pat dry with paper towel.
Cook the Chicken - Heat a large skillet over medium heat and add vegetable oil. Once the oil is hot, add the chicken. Cook for 6 to 7 minutes on the first side, then flip and cook for another 4 to 5 minutes, or until the chicken is cooked through and the outside is golden brown.
Prepare the toppings - While the chicken cooks, toss together the shredded Gruyère, white Cheddar, Parmesan, and Fontina cheeses. In a small bowl, combine the Panko breadcrumbs with the melted butter and stir until the crumbs are evenly coated.
Make the Cheese Sauce - For a rich cheese sauce, heat the heavy cream and 1/2 cup of the cheese blend in a small skillet over low heat. Stir until the cheese melts into a smooth sauce.
Assemble and Broil - Preheat your oven broiler. Place the cooked chicken on an oven-safe dish. Top each piece with about 1 tablespoon of cheese sauce (if using), followed by a generous handful of the cheese blend, and finish with a layer of buttered Panko breadcrumbs.
Finish Under the Broiler - Broil for 3 to 4 minutes or until the cheese is melted and beginning to brown. Watch closely to avoid burning. Serve hot.