Coat a Dutch oven with nonstick cooking spray. Add onion, mushrooms, and garlic. Cook and stir for 2 to 3 minutes or until vegetables are tender.
Add undrained tomatoes, beef broth, the 3/4 cup water, the tomato sauce, tomato paste, wine, dried basil, dried oregano, sugar, dried thyme, 1/4 teaspoon pepper, and the bay leaf. Bring to boiling; reduce the heat. Cover and simmer for 30 minutes.
Meanwhile, in a medium bowl, stir together egg white, bread crumbs, marjoram, 1/4 teaspoon pepper, and the salt. Add ground turkey and ground beef; mix well. Shape the mixture into 36 meatballs.
Place meatballs in a 12x7x2-inch (2-quart rectangular) baking dish. Bake in a 375 degree F oven for 15 to 20 minutes or until done (165 degree F). Drain the meatballs on paper towels. Add meatballs to tomato mixture. Return to boiling; reduce heat. Simmer, uncovered, for 10 minutes.
Meanwhile, cook the spaghetti according to package directions, except omit any cooking oil and salt. During the last 5 minutes of cooking, add the fresh broccoli and carrots to the spaghetti. Return the water to boiling. Cook about 5 minutes more or until the vegetables are crisp-tender and the spaghetti is tender, but firm (al dente). Drain.
Stir together cornstarch and the 1 tablespoon cold water. Stir into tomato mixture. Cook and stir until thickened and bubbly. Cook and stir for 2 minutes more. Remove and discard the bay leaf.
Serve tomato mixture and meatballs over spaghetti and vegetables. Sprinkle with Parmesan cheese, if you like. Makes 6 servings.