Combine the sun-dried tomatoes and boiling water in a bowl; let stand 30 minutes. Drain sun-dried tomatoes through a sieve into a bowl, reserving sun-dried tomatoes and soaking liquid. Cut tomatoes into julienne strips.
Heat oil in a large Dutch oven over medium-high heat. Add sun-dried tomatoes, ham, and next 4 ingredients (ham through garlic), and sauté 5 minutes. Add reserved soaking liquid, 6 cups water, and diced tomatoes; bring to a boil. Cover, reduce heat, and simmer 30 minutes. Add zucchini and beans; cook 5 minutes. Stir in basil, salt, and pepper. Place pasta into each of 7 large bowls; top with broth mixture and cheese.