Heat 1 tablespoon of olive oil in a large skillet over medium heat. Add 1 pound of ground chicken, breaking it apart with a wooden spoon. Cook for about 5–7 minutes or until the meat is no longer pink, stirring occasionally to ensure even cooking.

Stir in one finely chopped onion, cooking until it becomes translucent, about 3–4 minutes. Next, add 2 cloves of minced garlic and 2 tablespoons of Cajun seasoning, sautéing for an additional minute.

Mix in 2 tablespoons of tomato paste until it coats the chicken. Follow with 1 cup of low-sodium chicken broth, 1 cup of tomato sauce, and 1 tablespoon of Worcestershire sauce. Bring to a gentle simmer, uncovered, cooking for 8–10 minutes until the mixture thickens.

In a separate saucepan, melt 2 tablespoons of unsalted butter over medium heat. Whisk in 2 tablespoons of all-purpose flour to create a roux, cooking for about 2 minutes until lightly golden.

Gradually add 1 cup of whole milk, stirring continuously until the sauce thickens and coats the back of a spoon, around 4–5 minutes.

Once thickened, reduce the heat to low and stir in 1 cup of shredded sharp cheddar cheese and ½ teaspoon of paprika. Mix until the cheese is completely melted and the sauce is smooth.

Lightly toast the inner sides of brioche hamburger buns until golden brown. Generously spoon the Cajun chicken mixture onto the bottom half of each bun, then drizzle with warm cheese sauce. Top with the other half of the bun, serve immediately.