Heat oil over medium heat in a large dutch oven. Once hot, add onion, garlic, celery, and carrots and cook until the veggies have started to soften, about 5 minutes.
Add in the potatoes, canned tomatoes, cannellini beans, kidney beans, salt, black pepper, Italian seasoning, bay leaf, red pepper, and thyme.
Pour in vegetable broth and mix, making sure to scrape up all of the bits from the bottom of the pan.
Cover and bring to a boil over high heat. Reduce heat to low and let simmer for 15 minutes, or until potatoes are tender. Add in green beans and kale, and continue to simmer until green beans are tender. Taste and adjust seasoning.
Meanwhile, cook pasta according to the package directions, drain and set aside.
Serve soup warm with pasta.