Lay the chicken breast on a cutting board and cover with a large piece of parchment paper. Using a meat mallet or a heavy-bottomed skillet, pound the chicken until ½ inch thick. Generously season with salt and pepper.
Arrange three shallow bowls, and in the first, combine the flour and a pinch of salt. In the second, whisk the egg with the Dijon mustard. In the third, mix the panko, Parmesan, a generous pinch of salt, and the sesame seeds (if using).
Dredge the chicken in the flour, shaking off any excess. Dip into the egg mixture, turning to coat both sides, then transfer to the breadcrumb-Parmesan mixture and press firmly so the crumbs adhere.
Heat ¼ inch of neutral oil in a large cast-iron skillet over medium heat.
Once the oil reaches 375ºF, add the chicken. Cook until golden brown and crisp, about 3 to 4 minutes per side. When the internal temperature reaches 165ºF, transfer to a paper towel–lined plate and immediately season with a pinch of salt. Rest for 3 to 4 minutes before serving.
Meanwhile, in a mixing bowl, combine the romaine, radish, and Simple Lemon Vinaigrette. Season with salt and pepper to taste and toss until well combined.
Transfer the chicken cutlets to a plate and spoon the salad over the top. Garnish with additional Parmesan, freshly ground black pepper, and lemon wedges for squeezing.