Heat a large skillet over medium-high heat. Cook and stir sausage in the hot skillet until browned and crumbly, 5 to 7 minutes. Add onion and garlic; sauté until onion is tender and translucent, 3 to 5 minutes. Drain and discard grease.

Place potatoes in a slow cooker; add cooked sausage and onion mixture. Season with salt, black pepper, and red pepper flakes. Pour in chicken broth and up to 2 cups water to completely cover potatoes. Stir soup gently and cover.

Cook on Low for 5 to 6 hours or High for 3 to 4 hours.

Pour in heavy cream and stir in kale to combine. Cover and cook on High until flavors are incorporated, about 30 minutes more. Garnish with Parmesan cheese.