Heat olive oil over medium heat in a large pot. Add onions, celery, and carrots and cook until softened, about 8 minutes. Add garlic, Italian seasoning, smoked paprika, and tomato paste, cook one minute longer.
Add the bay leaf, chicken broth, white beans, and ham to the pot. Bring to a boil, cover with a lid, reduce heat to low, and cook for 20-25 minutes.
Stir together half and half or coconut milk and cornstarch. Stir into soup, add hot sauce, salt and pepper, and cook for five minutes longer to thicken.
Serve and enjoy.