If using sausage links, remove the casing and discard. Heat a large skillet over medium heat. Add the sausage and cook while breaking it up with a spatula until brown and crumbly. Discard the cooking fat and add sausage to the bottom of the slow cooker.
Top the sausage with the potatoes, broccoli, onion, garlic, salt, pepper, and broth. Cook on high for 4 hours or on low for 7 to 8 hours, until the veggies are tender when pierced with a fork.
Stir in the cream until smooth. Serve warm topped with crispy croutons (if desired).