In a large skillet, heat 1 tablespoon of olive oil over medium-high heat. Once hot, add 1 pound of ground chicken, breaking it up with a spatula. Cook for about 5-7 minutes until the chicken is browned and no longer pink, stirring occasionally to ensure even cooking. Once cooked, transfer the chicken to a plate and set aside.

In the same skillet, add another tablespoon of olive oil if needed, then toss in 1 finely chopped onion. Sauté for 3-4 minutes until the onion is translucent. Add 2 minced garlic cloves and 2 tablespoons of Cajun seasoning, stirring for an additional minute until fragrant.

Return the cooked ground chicken to the skillet, mixing in 1 tablespoon of tomato paste until glossy and combined. Pour in ½ cup low-sodium chicken broth and ½ cup canned tomato sauce, then add 1 tablespoon of Worcestershire sauce. Let this simmer uncovered for 8-10 minutes, stirring occasionally until the mixture is thick and spoonable, seasoning with salt and optional 1 teaspoon of brown sugar as desired.

In a separate saucepan, melt 2 tablespoons of unsalted butter over medium heat. Whisk in 2 tablespoons of all-purpose flour, stirring for about 1 minute to create a roux. Gradually add in 1 cup of whole milk while whisking constantly for 4-5 minutes, until it thickens and coats the back of a spoon. Stir in 8 ounces of freshly shredded cheese and ¼ teaspoon of paprika until melted and creamy, then season lightly with a pinch of salt.

While the cheese sauce is being prepared, split 4-6 brioche hamburger buns and butter the cut sides generously. Place the buns on a hot skillet or griddle, toasting them for about 1-2 minutes until golden brown and crisp.

To assemble, add a generous scoop of the Cajun chicken mixture onto the bottom bun. Ladle the creamy cheese sauce over the chicken. Top each creation with the other half of the toasted bun and serve immediately.