In a large pot, heat the olive oil over medium heat. Add the diced onion and sauté until it becomes translucent (about 5 minutes).
Add the minced garlic, and stir for another minute until fragrant.
Crumble in the Italian sausage and cook, stirring occasionally, until browned and cooked through (about 7-10 minutes).
Stir in the sliced carrots and celery, cooking for another 5 minutes until they start to soften.
Add the diced potatoes, chicken broth, diced tomatoes, oregano, and thyme. Bring the mixture to a boil, then reduce heat and let it simmer for 25 minutes or until the potatoes are tender.
Add the chopped kale or spinach, and simmer for an additional 5 minutes until the greens are wilted and tender.
Season the soup with salt and pepper to taste.
Serve hot, garnished with grated Parmesan cheese on top.