Heat the olive oil in a large pot over medium heat. Add the Italian sausage, breaking it up with a spoon as it cooks, until browned and cooked through.

Add the diced onion, carrots, and celery to the pot. Sauté until the vegetables begin to soften, about 5 minutes. Stir in the minced garlic and cook for another minute.

Sprinkle in the Italian seasoning and thyme (if using), and stir to coat the veggies and sausage. Pour in the chicken broth and add the drained white beans.

Bring the mixture to a gentle boil, then reduce heat to low and simmer uncovered for about 20–25 minutes, allowing the flavors to meld and the vegetables to soften.

Stir in the chopped kale or spinach and simmer for another 3–5 minutes until the greens wilt and are tender.

Taste the soup and adjust the seasoning with salt and black pepper. Ladle into bowls and serve warm.