Heat a large skillet over medium-high heat. Add the ground chicken and break it into small crumbles as it cooks. Cook until fully browned with no pink remaining, about 6 to 8 minutes. Drain any excess liquid from the pan.

Add the diced green pepper, onion, and celery to the skillet. Cook for 5 to 7 minutes, stirring occasionally, until the vegetables are softened and the onion is translucent. Add the minced garlic and cook for 1 more minute until fragrant.

Stir in the tomato sauce, tomato paste, Worcestershire sauce, brown sugar, Cajun seasoning, and smoked paprika. Mix until fully combined and the tomato paste is evenly incorporated.

Reduce heat to low and simmer uncovered for 10 minutes, stirring occasionally, until the sauce thickens to a sloppy joe consistency. Add a splash of chicken broth or water if it becomes too thick. Taste and adjust seasoning.

While the filling simmers, butter the cut sides of each bun and toast in a skillet over medium heat or under the broiler for 1 to 2 minutes until golden brown.

Spoon a generous portion of the Cajun chicken filling onto each toasted bun. Top with sliced pickles or pickled jalapeños and serve immediately.