In a large pot over medium heat, add the Italian sausage. Cook until browned, breaking it apart with a spoon, about 5-7 minutes. Drain excess fat if necessary.
Add the diced onion and minced garlic to the pot. Sauté for about 3-4 minutes until the onion is translucent.
Pour in the chicken broth and add the diced potatoes, carrots, celery, thyme, paprika, salt, and pepper. Bring the mixture to a boil.
Reduce the heat to low and let it simmer for about 20-25 minutes, or until the potatoes and carrots are tender.
Stir in the heavy cream and shredded cheddar cheese, mixing until the cheese is melted and the soup is creamy. Heat for an additional 5 minutes.
Serve hot, garnished with chopped parsley.