Set up a 3 part breading station. In the first dish, combine the flour with 1/2 teaspoon salt and 1/4 teaspoon freshly ground black pepper. In the second dish, beat 2 eggs with 1 tablespoon oil, 1/2 teaspoon salt and 1/4 teaspoon freshly ground black pepper. In the third dish, pour in 2 cups of panko crumbs and mix with 1 1/2 teaspoons salt.
Sprinkle salt over both sides of chicken and dredge each breast in the flour, shaking off the excess. Then, dip into the egg mixture, making sure that they are totally coated. Finally, place the chicken in the panko crumbs, pressing the crumbs into both the top and bottom surfaces. Move the coated breast to a wire rack to allow the crumbs to dry.
Place a very large (12-inch) skillet over medium-high heat. Add 1/2 the frying oil to the skillet and raise the heat to medium-high. Once the oil is hot, place two of the breasts into the pan and cook until both sides are golden brown, about 5 to 6 minutes total. Remove to a warm plate lined with paper towels. Add the remaining frying oil, and saute the last two breasts.
Spoon the salsa over the breasts and serve without delay.