Preheat the oven to 350 degrees F. Tear off 2 pieces of foil about 12 inches longer than the baguette and stack on top of each other.
Cut the chicken crosswise into 4 equal pieces. Set up a breading station with 3 shallow dishes: Stir together the flour and 1 teaspoon salt in the first dish; beat the egg and 3 tablespoons of the hot sauce in the second dish and add the breadcrumbs to the third dish. Coat each strip of chicken first in the flour, then dip in the egg mixture, letting any excess drip off. Then press into the breadcrumbs. Transfer to a plate.
Line a second plate with a paper towel. Heat the oil in a large skillet over medium heat until a piece of the breading sizzles when added. Add the breaded chicken to the oil, making sure the pieces don't touch. Fry until golden brown on both sides, 2 to 3 minutes per side. Remove to the lined plate.
Cut the baguette into 4 equal pieces (about the same length as the chicken pieces). Use a paring knife to hollow out the insides of each piece of baguette.
Lay a piece of chicken on top of a slice of mozzarella and dash with a little more hot sauce if desired. Wrap the cheese around the chicken and stuff inside one of the baguette pieces. Repeat with the remaining chicken, cheese, hot sauce (if using) and bread pieces. Slice each stuffed baguette piece into thirds and arrange them together tightly on top of the foil.
Put the butter, garlic and remaining 1 tablespoon hot sauce in a microwave-safe bowl and microwave in 30-second intervals, stirring between each, until the butter is melted. Pour the mixture over the top of the baguette pieces and fold the foil over to enclose the baguette.
Bake until the chicken is cooked through, the cheese is melted and the top of the bread is starting to turn brown, 30 to 35 minutes. Transfer the foil pack to a cutting board and unwrap. Serve with carrots, celery, hot sauce and blue cheese dressing on the side.
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