Heat 2 tablespoons olive oil and garlic in a large saucepan over medium-high heat. Sauté garlic, stirring occasionally, for 2-3 minutes or just until garlic starts to turn golden brown.
Add chopped onion, carrot, and celery and cook for another 4-5 minutes, stirring occasionally, or until vegetables are soft and tender.
Add diced tomatoes, cannellini beans, 4 cups vegetable broth, bay leaves, rosemary, thyme, oregano, and red pepper flakes to pan and stir to combine. Add Parmesan cheese rind, if using, and season with salt and black pepper, to taste.
Bring to a boil, then reduce heat to medium-low. Cover and simmer 20-25 minutes.
While soup is simmering, cook pasta according to package directions until al dente. Reserve 1 cup of the cooking liquid before draining pasta. Rinse pasta and transfer to a medium bowl and toss with remaining olive oil. Cover and set aside.
Remove lid from pan and add the green beans and the reserved pasta cooking liquid. Stir to combine and continue cooking, uncovered, another 20-25 minutes or until green beans are tender.
Add arugula and additional vegetable broth, if needed, and stir to combine. Season with additional salt and pepper, to taste. Cook for 2-3 minutes or until arugula begins to wilt.
To serve, divide cooked pasta among individual serving bowls and top with hot soup. Top with chopped
parsley and freshly grated Parmesan cheese, if desired. Serve with crusty bread for a hearty meal. Enjoy!