In a large skillet, heat 1 tablespoon of oil and 1 tablespoon of butter over medium-low heat. Add the finely chopped onion, celery, and bell pepper, cooking for about 7-8 minutes until the vegetables soften and become fragrant.

Increase the heat to medium and add 1 pound of ground chicken, breaking it apart. Cook for approximately 5 minutes until browned. Add 2 tablespoons of Cajun seasoning and 3 minced garlic cloves, stirring for another minute.

Stir in ½ cup of crushed tomatoes and ½ tablespoon of brown sugar. Add ½ to 1 teaspoon of hot sauce. Pour in ½ cup of heavy cream and reduce the heat to low.

Allow the mixture to simmer on low for about 15 minutes, stirring frequently. Taste and adjust with ¼ teaspoon of salt.

Butter the insides of the 4 burger rolls and toast them until golden and crispy.

Spoon generous amounts of the Cajun chicken mixture onto the toasted rolls. Serve immediately.