Melt the oil and butter in a large skillet over medium-low heat.

Add the chopped onion, celery, and bell pepper. Cook for 7-8 minutes until softened.

Add the ground chicken and cook, breaking it up as you go. Cook for 5 minutes until the chicken changes color, then sprinkle over the cajun seasoning and minced garlic.

Cook for 1 minute, ensuring the garlic does not change color.

Add the crushed tomatoes, brown sugar, hot sauce, and heavy cream, then mix well and reduce the heat to low.

Cook for 15 minutes, stirring frequently to prevent sticking.

Taste the mixture and add salt to taste.

Toast the burger rolls and serve.