Line a cutting board with plastic wrap. Cut each chicken breast in half lengthwise to make 4 thin cutlets. Place the chicken in a single layer on the cutting board and cover with a second sheet of plastic wrap. Use a meat mallet, rolling pin or the bottom of a heavy saucepan to pound the chicken thin, about ¼ inch thick. Cut each cutlet in half for 8 cutlets total.
Set up three medium bowls: In the first, whisk together the flour, garlic salt, paprika and pepper. In the second, add the eggs and thoroughly beat with a fork. In the third, add the panko.
Dredge both sides of 1 cutlet in the flour to coat well, then in the egg, letting any excess drip back into the bowl before breading the chicken in the panko. It helps to use a fork or tongs for this process to keep your hands clean. Transfer the breaded cutlet to a platter or baking sheet. Repeat with the remaining cutlets, keeping them in a single layer on the platter. If you have time, let the breaded chicken rest for 10 minutes, which will help the coating stick better.
Heat a large nonstick pan over medium heat and add just enough oil to coat the bottom, about 3 tbsp. When the oil shimmers, add a few cutlets to the pan, being careful not to crowd them. Cook for 3 to 4 minutes per side, until crispy and golden and an instant-read thermometer registers 165°F. (You can also slice one open; the juices should run clear and the meat should no longer be pink.) Reduce the heat if the cutlets are browning too quickly. Transfer the cutlets to a paper towel-lined plate and immediately sprinkle the cutlets with the salt. Repeat with the remaining cutlets, adding more oil to the pan as needed.
Serve immediately with a sprinkle of parsley and the lemon wedges.