Heat olive oil and butter in a large pan over medium heat. Add onion, garlic, Italian seasoning, and smoked paprika. Cook for 1–2 minutes until fragrant, creating a flavorful base.
Stir in butter beans, vegetable stock, and bay leaves. Simmer gently for 10–15 minutes to allow the beans to absorb flavors. This step develops a rich, savory broth.
Add chopped kale and cook until wilted. Stir in heavy cream and balsamic vinegar to create a creamy, velvety texture. Taste and season with salt and pepper as needed.
Remove bay leaves, ladle into bowls, and garnish with parsley, shaved Parmesan, and toasted sourdough. Serve immediately for a warm, comforting meal.