Heat olive oil and butter in a large pan. Sauté onion for 2–3 minutes.
Add cherry tomatoes, sun-dried tomatoes, salt, pepper, oregano, and garlic powder. Cook 5 minutes, until tomatoes soften.
Stir in heavy cream, broth, butter beans, and Parmesan. Simmer 2–3 minutes, then add kale and cook until wilted.
Remove from heat and gently stir in burrata until creamy and melted through.
Serve warm with crusty bread or pasta.
