Cover the chicken breasts with plastic wrap and gently pound the chicken out to 1/4-inch thickness. Sprinkle the chicken with salt.
Heat a large skillet over medium-high heat to 360 degrees F.
Season the flour with salt in a small bowl. Combine the panko and Parmesan in a small bowl. Begin breading the chicken by dredging it in the flour, then the beaten eggs, then the panko mixture, shaking off any excess in between. Let sit at room temperature for up to 30 minutes.
Add the oil to the hot skillet, followed by 2 pieces of chicken. Cook until golden brown and crisp on both sides and the chicken is cooked through, 2 to 3 minutes per side. Remove the chicken to a wire rack and season it lightly with salt. Repeat with the remaining chicken, adding more oil to the pan as necessary.
Serve with a lemon wedge on top of each piece of chicken.