Make the buffalo sauce by whisking together the hot sauce, melted butter, ketchup, vinegar, Worcestershire sauce and celery salt. Split it between two bowls, and save half for later.
Mix the blue cheese dip ingredients together with a fork, then chill until needed.
Butterfly the chicken breast, then place it skin(-less) side down, on a large piece of non stick baking paper on top of a wooden chopping board. Put another piece of baking paper on the top, then use a rolling pin to flatten the chicken breast. Try to get it less than 1 cm thin across the whole breast, but be careful not to go to far and make holes in it.
Spoon a tablespoon of buffalo sauce onto the chicken and spread it around with the back of a spoon.
Lay thin slices of mozzarella on one half of the chicken breast, leaving a 1.5cm gap at the edge, and sprinkle a large handful of grated cheese on top of that. Then fold the top of the chicken breast over and press the edges down to loosely seal it, tucking any pieces of cheese inside.
Heat a cast iron pan. Brush the top of the chicken with buffalo sauce, then place it sauce side down in the hot pan. Brush the top with hot sauce and cook for 3-4 minutes, until the chicken is cooked through. Brush the chicken again with buffalo sauce then carefully turn it over to cook the other side for another 3-4 minutes, until the chicken is fully cooked and no longer pink.
Serve immediately alongside the reserved buffalo sauce, with celery sticks and blue cheese sauce on the side.