In a large skillet, heat olive oil over medium heat. Add ground chicken and cook until browned, breaking it up as it cooks, about 5-6 minutes.
Add chopped onion, bell pepper, and garlic. Saut? until the vegetables are soft, about 3-4 minutes.
Sprinkle in Cajun seasoning, salt, and pepper. Stir well to coat everything. Add chicken broth and simmer for 5 minutes, until the mixture slightly thickens.
Pour in heavy cream, stirring until smooth. Gradually add shredded cheddar cheese, stirring until melted and creamy.
Toast buns lightly if desired. Spoon the Cajun chicken mixture generously onto the bottom half of each bun, then top with the other half.
Enjoy your Cajun Chicken Sloppy Joe while it?s hot and gooey!