Place a large 6-8 quart pot over medium-high heat. Add the peppers and sear in a dry pan for 2 minutes, to char the edges. Then scoop out of the pot and set aside.
Next add 1 tablespoon butter, onions, and garlic. Sauté for 2-3 minutes and toss the beef pieces, 1 1/2 teaspoons salt, 1/2 teaspoon ground black pepper. Stir and brown the beef, until seared on all sides. Then stir in the mushrooms, potatoes, bell peppers, broth, thyme, and cognac.
Bring the soup to a boil. Cover the pot with a heavy lid, and lower the heat to simmer. Simmer the soup for 1 hour, or until the beef is very tender.
Meanwhile, preheat the oven to 400 degrees F. Cut twelve 1-inch slices from a wide loaf of French bread. Spread the remaining butter over the bread slices. Bake the bread until the toast is crisp, about 5 minutes. Then cover each piece of toast with a slice of provolone cheese. Place back in the oven for 3 minutes, or until the cheese melts.
To Serve: Ladle the soup into bowls. Then place one piece of cheese toast over the top of each bowl, French onion soup style.