In a saucepan over medium-high heat, heat sugar and 2 teaspoons vinegar until they form a 'cola' color, about 6 to 8 minutes. Add in 1/3 cup vinegar and reduce to a syrup, 5 to 6 minutes. Add 1 cup red wine and reduce to a thin syrup, about 8 to 10 minutes. Add beef stock, reduce heat to medium and simmer for 15 to 20 minutes. Remove from heat and set aside.
Heat 2/3 cup olive oil in a large sauté pan over medium heat then add shallots and garlic then cook for 5 minutes or until translucent. Add prosciutto and mushrooms then cook for 8 minutes, stirring occasionally. Remove and allow mixture to sit on a plate covered with paper towels.
Return empty sauté pan to medium heat. Melt butter and add mushroom-prosciutto mixture. Stir in vinegar reduction, Marsala wine, brown gravy and tarragon. Bring to a simmer and cook 15 to 20 minutes.
Preheat oven to 260 degrees C.
Meanwhile, place flour, salt and pepper in a plastic bag or shallow baking dish. Dredge each steak with flour and set aside. In a new frying pan, heat 1/2 cup olive oil over medium-high heat. Add floured steak and cook until golden on both sides, about 2 minutes each side. Remove meat to a plate with paper towels to drain.
Spoon half of prosciutto-mushroom sauce into a 22 x 33cm baking dish, cover with steaks, top with remaining sauce and slices of mozzarella. Bake in oven for 10 minutes or until cheese is hot and bubbling.