Cut the boneless chicken into small, evenly sized pieces. Season with salt, black pepper, garlic powder, and paprika, mixing well to coat all sides.
In one bowl, whisk together the egg and milk. In a second bowl, combine the all-purpose flour and cornstarch.
Dip each piece of seasoned chicken into the egg mixture, then coat thoroughly in the flour mixture.
Heat oil in a deep pan over medium heat. Fry the coated chicken in batches until golden brown and fully cooked. Remove and drain on paper towels.
While the chicken cools slightly, prepare the cheese by shredding the mozzarella and cheddar.
Slice the buns open without cutting all the way through. Fill each bun with fried chicken, then top generously with cheese.
Heat a shallow layer of oil in a pan over low to medium heat. Place the stuffed buns seam-side down and fry slowly, turning carefully, until all sides are golden and crisp and the cheese has melted.
Remove from the pan and let the buns rest for 1 to 2 minutes before serving.
