Place the chicken breast in a small saucepan and cover with water. Bring to a boil, then reduce heat and simmer for 10-15 minutes, or until cooked through. The internal temperature should reach 165°F (74°C). Remove the chicken, let it cool slightly, and shred it with two forks.
While the chicken cooks, heat 1 tablespoon of oil in a skillet over medium heat. Add the chopped onion and bell pepper and cook until softened, about 5-7 minutes.
In a medium bowl, combine the shredded chicken, cooked vegetables, mayonnaise, soy sauce, Italian seasoning, paprika, pepper, salt, and shredded mozzarella. Stir until everything is well mixed.
Trim the crusts from all sides of each bread slice. Use a rolling pin to flatten each slice until it is very thin.
Spoon about 2 tablespoons of the chicken filling onto one end of a flattened bread slice. Roll it up tightly into a log shape. Pinch the seam and the ends to seal them completely.
Prepare three shallow dishes. Place the flour in the first, beat the eggs in the second, and put the panko breadcrumbs in the third.
Carefully coat each chicken roll first in the flour, then dip it in the beaten egg, and finally press it into the panko breadcrumbs until it is fully coated.
Pour about 2 inches of vegetable oil into a heavy-bottomed pot or deep skillet. Heat the oil to 350°F (175°C). Fry the rolls in batches, turning occasionally, for 2-4 minutes or until they are golden brown on all sides.
Use a slotted spoon to transfer the cooked rolls to a wire rack or a plate lined with paper towels to drain excess oil. Serve warm.