Heat the olive oil in a large pot over medium-high heat. Add the onion and cook until translucent, about 4 minutes. Add the garlic and cook 30 seconds. Add the celery and carrot and cook until they begin to soften, about 5 minutes. Stir in the dried oregano and basil, 3/4 teaspoon salt, and pepper to taste; cook 3 more minutes.
Add the can of tomatoes crushing with your hands and the vegetable broth to the pot and bring to a boil. Reduce the heat to medium low and simmer 10 minutes. Stir in the kidney beans, savoy cabbage, and pasta and cook until the pasta and vegetables are tender, about 10 minutes. Season with salt. Ladle into bowls and top with the parmesan and chopped basil.