In a large pot, heat a drizzle of olive oil over medium heat. Cook Italian sausage until browned, breaking into crumbles. Remove excess grease if necessary.
Add onion and garlic, sauté until fragrant and softened, about 3 minutes.
Stir in potatoes, chicken broth, and red pepper flakes. Bring to a boil, then reduce heat and simmer for 15–20 minutes, until potatoes are tender.
Stir in chopped kale and heavy cream. Simmer for 5 more minutes until kale is tender and soup is heated through.
Season with salt and pepper to taste. Serve hot with crusty bread.