Heat the olive oil in a large skillet over medium heat. Add the ground chicken and cook for 7 to 10 minutes, breaking it apart as it cooks until no longer pink. Set aside.
In the same skillet, add the chopped onion and diced bell pepper. Sauté for 5 minutes until soft. Stir in minced garlic and cook for 1 minute.
Add the cooked ground chicken back into the skillet. Sprinkle in Cajun seasoning and smoked paprika, stirring well to coat.
Pour in chicken broth, Worcestershire sauce, and tomato paste. Stir until well combined and bring to a simmer. Reduce heat to low and let simmer for 10 minutes.
Toast the hamburger buns if desired. Spoon the mixture onto the bottom half of each bun, top with chopped green onions, and serve immediately.