Heat the oven to 375°F. Lightly grease 8 cups of a standard muffin tin.
In a large bowl, combine the ground chicken, egg, panko, 2 tablespoons of the hot sauce, diced celery, diced onion, garlic powder, and salt. Mix gently until just combined.
Divide the mixture among the 8 prepared muffin cups. Press it lightly into each cup, leaving the tops slightly rounded. Brush the remaining 2 tablespoons of hot sauce over the tops.
Bake for 20 to 25 minutes, until the muffins are cooked through and the centers reach 165°F. Let them rest in the tin for 5 minutes before removing.
While the muffins bake, whisk together the mayonnaise, apple cider vinegar, and honey in a medium bowl. Add the sliced celery and shredded carrots, then toss to coat.
Serve the warm chicken muffins with the celery slaw on the side or spooned over the top.