Brown the Italian sausage in a skillet over medium heat until fully cooked. Drain excess grease.
Transfer the cooked sausage to the crockpot.
Add sliced potatoes, diced onion, minced garlic, and chicken broth to the slow cooker. Stir to combine.
Cover and cook on LOW for 5–6 hours until potatoes are fork-tender.
Stir in the heavy cream and chopped kale.
Add Parmesan cheese, salt, and black pepper.
Cover and cook for an additional 15–20 minutes until kale is tender.
Let the soup rest for a few minutes before serving.