In a large pot over medium heat, add the olive oil. Add the onion, celery, and carrots. Cook and stir for 4 to 5 minutes or until the onions are softened. Add the garlic and continue to cook and stir for 1 more minute.
Increase the heat to medium-high and add the red potatoes, vegetable broth, water, salt, pepper, and crushed red pepper. Once the mixture starts to boil, reduce the heat to medium, cover, and allow to simmer for 20 to 30 minutes or until the potatoes are fork tender.
Add the beans, kale, and heavy cream. Stir frequently until the kale has wilted. Add additional salt and pepper if desired.
Serve with a generous helping of freshly grated parmesan cheese on top.