Peel and cut the eggs in half. Place the yolks into a medium bowl and the whites on a 9×13 inch cookie sheet lined with wax paper.
Mash the yolks finely using a fork then add in the mayonnaise, Dijon mustard, hot sauce, sweet pickle relish, salt and pepper. Stir until well combined. Taste for more seasoning.
Pour the oil into a large skillet, pot, or deep fryer and bring to about 350F degrees.
Dollop the egg whites with a little of the filling (do not add a lot).
Add the flour and season with salt and pepper in a round pan or medium bowl, the eggs in one, and the panko breadcrumbs in the other; dip the eggs into the flour (shake off the access), then in the eggs (shake off the access) and finally into the panko.
Gently place the eggs into the hot oil and fry until golden brown about 3 to 4 minutes. Remove the eggs from the oil and drain them onto a pan lined with paper towels. Season with salt and pepper.
Place the fried eggs onto a platter, sprinkle with chopped parsley (if desired) and enjoy.
