Heat 1 tablespoon of olive oil in a large skillet over medium heat. Add chopped chicken, season with salt and pepper, and cook for 5–7 minutes, stirring occasionally.
Add diced onion, bell pepper, and minced garlic to the skillet. Cook for 3–4 minutes until softened and aromatic, stirring often.
Stir in Cajun seasoning, smoked paprika, Worcestershire sauce, and tomato paste. Cook for 1 minute to let the spices bloom.
Add drained diced tomatoes, chicken broth, brown sugar, and hot sauce (if using). Simmer uncovered for 10 minutes, stirring occasionally. Add more broth if the sauce thickens too much.
Toast your buns for 1–2 minutes. Spoon the chicken mixture onto each bun, top with shredded cheddar cheese (optional), and serve hot!