Buffuletta bread roll: weigh and add all your ingredients to a large bowl or the bowl of your stand mixer. If you are kneading with a mixer, mix on medium speed for 8 minutes. If you are kneading by hand, you must knead it for around 10 or 15 minutes to get a smooth dough.
Add dough to a lightly oiled bowl and place it in a warm spot in your kitchen. Allow to rise for 1 to 1.5 hours.
After the dough has more than doubled, remove it from the bowl and attempt to shape it into a smooth, round ball. With your hands or a rolling pin, flatten that ball into a flat disk shape that is less than an inch thick and about 8 to 9 inches in diameter. Carefully move this disk to a parchment-lined sheet pan. Cover the dough with a piece of plastic wrap and allow it to rise again for another 30 to 45 minutes.
Near the end of the final rise time, preheat your oven to 400 degrees F (204 C).
Remove the plastic wrap from the dough. Create an egg white wash by adding an egg white and 1 tablespoon of water to a small bowl. Whisk to combine. Paint the top of your dough very well with the egg white wash. Once the dough is fully painted in egg white wash, sprinkle a liberal amount of sesame seeds on top.
Bake the bread for 25 to 30 minutes, rotating the pan 180 degrees at the halfway point.
Allow bread to cool fully before slicing.
Pickled celery and carrot: add apple cider vinegar, water, sugar, and salt to a small pot over medium heat.
Bring mixture to boil while you prepare and cut your carrots and celery and place them in a medium bowl.
When the liquid starts to boil, remove the heat and stir until everything is combined and dissolved. Pour the liquid over the top of your veggies.
Allow the vegetables to cool on the counter and then add them to a sealed container and store them in the refrigerator for up to a month.
Fried chicken: add salt, pepper cayenne pepper, and paprika to buttermilk (add hot sauce if you want extra spice). and whisk to combine. Put chicken in a zip-top bag or bowl with a lid. Pour buttermilk marinade over the chicken and store in the fridge for at least an hour or overnight.
Make seasoned flour by combining flour with all the spices, salt, and pepper in a bowl or pan that is large enough for a piece of chicken to lay flat in the flour.
Remove one piece of chicken at a time from the marinade and dredge in the seasoned flour mixture until thoroughly coated on all sides. Place the fully coated chicken onto a piece of parchment or a sheet pan rack to rest.
Heat 2 inches of peanut oil in a skillet to 350 degrees F (175 degrees C).
Fry each piece of chicken for 6 to 7 minutes or until it reaches 165 degrees internal temperature. You'll probably want to fry for 3 minutes on the first side and then flip it to make sure you're getting the level of browning that you want. Continue cooking on the other side.
After frying, place the finished chicken on a cooling rack over paper towels to drain some of the oil away.
Sandwich assembly: you can either toss the chicken in buffalo sauce or you can just pour the sauce onto the sandwich on top of the chicken. Either way should work about the same. I made sure to slice each chicken thigh on the diagonal to make it a bit easier to eat in the final sandwich.
Slice the buffuletta roll horizontally to prepare it for sandwiching.
Add some buffalo sauce to the bottom roll and then top the sauced bottom roll with all your chicken.
Top the chicken with more sauce unless you already tossed it in the sauce. Top the chicken with slices of mozzarella. Then top the mozzarella with a healthy amount of pickled veggies.
Add the buffuletta roll to the top to complete the sandwich.
Slice into quarters and serve.