Make caramel sauce: Place sugar and water in heavy-bottomed saucepan. Heat over high heat without stirring until mixture begins to caramelize and becomes a light amber color. Remove from heat and CAREFULLY add cream, stirring briskly, a little at a time. The mixture will bubble and "erupt" until sugar cools a bit. When all cream is added, return to heat and simmer 1-2 minutes. Add salt and set aside.
Heat sauté pan over high heat. Melt 1 tablespoon butter in pan; add sliced apples and cook for 2 minutes. Remove from heat and add brandy, if using. Return to heat and cook until alcohol has burned off. Be careful the brandy does not come in contact with flame of gas stove and catch fire. Keep apples warm.
Heat griddle or nonstick pan over medium heat. Add 1-2 tablespoons butter; melt. Add brioche slices and top with a slice of Cheddar. Grill until cheese melts. Meanwhile, place 1 tablespoon of caramel sauce on each serving plate. Place the Cheddar-brioche slices over sauce. Top with apple/brandy mixture and drizzle with more caramel sauce.