Brown the sausage: Heat a large soup pot or Dutch oven over medium heat. Add sausage and cook, breaking it up with a wooden spoon, until browned and cooked through. Transfer to a plate, leaving rendered fat in the pot. Add olive oil only if needed.
Add onion and cook 5–7 minutes until softened. Stir in garlic, red pepper flakes, and fennel seeds; cook 1 minute until fragrant.
Return sausage to the pot. Add chicken broth, water, potatoes, chickpeas, salt, and pepper. Bring to a simmer, then cover and cook 12–15 minutes, until potatoes are tender.
Stir in the torn kale and cook 3–4 minutes until wilted and softened.
Reduce heat to low. Stir in heavy cream and Parmesan until warmed through and silky. Taste and adjust with salt, pepper, or a squeeze of lemon for brightness.
Serve: ladle into bowls and top with more Parmesan, black pepper, and red pepper flakes if you like heat. Serve with crusty bread for dunking.