Heat olive oil in a large pot over medium heat. Add garlic, onion, carrots, and celery and cook until softened, about 5-7 minutes.
Add diced tomatoes, cannellini beans, vegetable broth, bay leaves, rosemary, thyme, oregano, red pepper flakes, salt, and pepper. Bring to a boil, then reduce heat and simmer for 20-25 minutes.
Add fusilli pasta and cook until al dente, about 8-10 minutes.
Stir in arugula and cook until wilted, about 1-2 minutes.
Remove bay leaves before serving. Ladle soup into bowls and garnish with grated Parmesan cheese.