Preheat oven to 375°F (190°C). Grease a baking dish.
Pound chicken breasts to an even thickness. Season with salt, pepper, garlic powder, onion powder, and smoked paprika.
In a pan, heat olive oil over medium heat. Add onions and butter, cooking until soft and caramelized. Add brown sugar for extra flavor.
Fill each chicken breast with mozzarella and cheddar cheese. Roll tightly and secure with toothpicks.
Place the stuffed chicken rolls in the baking dish. Pour chicken broth around them and bake for 25-30 minutes until cooked through.
In a saucepan, heat the remaining caramelized onions with dried thyme, oregano, and heavy cream. Simmer until thickened.
Remove chicken from the oven and top with the creamy caramelized onion sauce.
Serve hot and enjoy your cheesy stuffed chicken rolls!