Heat a large skillet over medium-high heat and add a splash of olive oil. Once it shimmers, introduce the ground chicken, cooking for 5-7 minutes until golden and no longer pink. Stir in finely chopped onion and cook for 3-4 minutes until translucent. Add minced garlic and Cajun seasoning, cooking until fragrant for about 1 minute before incorporating tomato paste until it glistens.

Pour in low-sodium chicken broth, tomato sauce, and Worcestershire sauce, stirring to combine. Bring to a gentle simmer, uncovered for 8-10 minutes until thickened. Taste and adjust seasoning with salt and brown sugar if desired.

In a separate saucepan, melt unsalted butter over medium heat, then whisk in all-purpose flour to create a pale roux, cooking for about 1 minute. Gradually whisk in whole milk, stirring constantly until thickened, about 4-5 minutes.

Once thickened, reduce heat and stir in freshly shredded sharp cheddar cheese and paprika until melted and smooth, careful not to let sauce boil.

Butter and toast cut sides of brioche buns on a skillet over low heat until golden and crispy, about 1-2 minutes. Spoon generous amounts of Cajun chicken filling onto each bottom bun, drizzle with cheese sauce, and finish with black pepper.

Cover each sloppy joe with the top bun and serve immediately while warm.