Prepare the sausage by removing casing if using links, then crumble it.
Chop onion, mince garlic, peel and dice potatoes, and chop kale after removing stems.
Heat olive oil in a large pot over medium heat.
Add sausage and cook, breaking into pieces, until browned and cooked through (5-7 minutes).
Drain excess fat leaving about 1 tablespoon for flavor if needed.
Add chopped onion and cook until translucent (about 5 minutes).
Add minced garlic and cook for another minute until fragrant.
Add red pepper flakes and dried thyme or Italian seasoning if using, stir to combine.
Pour in chicken broth, scraping up browned bits from the pot.
Add diced potatoes and bring to a boil, then reduce heat and simmer until potatoes are tender (15-20 minutes).
Stir in chopped kale and cook until wilted and tender (about 5 minutes).
Slowly add heavy cream or half-and-half, stirring gently to combine. Heat through without boiling.
Season with salt and pepper to taste.
Serve hot, optionally topped with grated Parmesan and accompanied by crusty bread.