In a large bowl combine the ground chicken, mesquite seasoning, Worcestershire sauce, diced onion, minced garlic, egg, panko breadcrumbs, kosher salt, and black pepper. Use your hands or a spoon to mix gently until just combined — do not overwork or the patties will become dense. Divide the mixture into 4 equal portions and shape each into a patty about 3/4" thick and slightly wider than the onion rolls to allow for shrinkage.

Chill (optional)

If time allows, place formed patties on a plate, cover, and refrigerate for 15–30 minutes to help them hold together when cooking.

Cook patties

Heat a large skillet or cast-iron pan over medium-high heat and add 2 tablespoons vegetable oil. When oil is shimmering, add the patties leaving space between them. Cook 4–5 minutes on the first side without moving until a golden-brown crust develops. Flip and cook an additional 4–5 minutes, or until internal temperature reaches 165°F (74°C). Reduce heat slightly if edges brown too quickly. Remove patties to a plate and tent loosely with foil to rest for 3–5 minutes.

Thousand Island Dressing

While patties cook (or ahead of time), make the dressing. In a small bowl whisk together the mayonnaise, ketchup, sweet pickle relish, apple cider vinegar, hot sauce (if using), salt, and black pepper until smooth. Taste and adjust seasoning — add more relish for sweetness or a pinch more vinegar for brightness. Refrigerate until ready to assemble.

Sandwich Assembly

Prepare rolls and vegetables

If you like toasted rolls, butter the cut sides of the onion rolls lightly. Place a skillet or griddle over medium heat and toast the buttered sides until golden, about 1–2 minutes. Meanwhile, rinse and dry lettuce leaves and slice the tomato into 4 even slices.

Assemble sandwiches

Spread about 1 tablespoon of the thousand island dressing on the bottom half of each toasted roll. Place a lettuce leaf (or two folded) on the dressing, add one chicken patty, then top the patty with a tomato slice. Spoon another tablespoon of dressing onto the tomato (or onto the top roll) and close the sandwich with the top half of the roll. Repeat for remaining sandwiches.

Serve

Serve the mesquite chicken sandwiches immediately while patties are warm. Offer extra dressing on the side and optional pickles or chips as accompaniments.