In a large skillet, heat olive oil over medium heat.
Add onion and bell pepper, cooking until softened (3-4 minutes). Add garlic and sauté for another minute.
Add ground chicken, breaking it up with a spatula. Season with Cajun seasoning, salt, and pepper. Cook until no longer pink (5-7 minutes).
Stir in chicken broth and heavy cream. Simmer for 2-3 minutes until slightly thickened.
Stir in cheddar and mozzarella cheese until melted and creamy.
Spoon mixture onto toasted burger buns. Serve hot with your favorite toppings.
