Heat 2 T. oil in heavy large saucepan over medium heat. Add onion, carrots and bell pepper. Cook until beginning to soften, stirring occasionally, about 8 minutes. Add ham, 3 T. fresh basil, garlic and oregano. Stir 2 minutes. Add tomatoes. Cook until mixture is reduced to thick sauce, about 6 minutes. Add broth and beans. Bring to boil, mashing 1/4 of beans against sides of pot. Reduce heat, cover and simmer 15 minutes.
Bring to boil, stirring occasionally. Add pasta. Boil gently until pasta is almost tender but firm to bite, 6-7 minutes. Season with salt and pepper. Sprinkle mushrooms over soup. Remove from heat, cover and let stand 5 minutes. Return soup to boil, stirring constantly. Adjust seasoning. Stir in 5 T. fresh basil. Ladle soup into bowls. Top with green onion tops and drizzle with oil. Pass Parmesan and freshly ground pepper separately.