Heat a skillet over medium heat and add the Italian sausage. Cook it while breaking it into crumbles until it is browned and no longer pink, about 6 minutes. Add the chopped onion and minced garlic to the skillet and cook for 3 more minutes until the onion softens.
Transfer the sausage mixture to the slow cooker. Add the diced potatoes, chicken broth, dried oregano, salt, and black pepper. Stir everything together to combine.
Cover the slow cooker and cook on low for 6 hours or on high for 3 hours until the potatoes are fork-tender.
Turn off the slow cooker and stir in the grated Parmesan cheese until it melts into the broth. Let the soup sit for 5 minutes to thicken slightly.
Ladle the soup into bowls and sprinkle each serving with the chopped fresh parsley.