Make the salad. In a large bowl, whisk the olive oil, lemon juice, lemon zest, salt and sugar together. Add the thinly sliced fennel, the peppers, and the parsley. Toss to combine. Set aside until ready to use.
Make the chicken schnitzel. Pound each chicken breast to ¼ inch thickness and season with salt and pepper.
Set out three large plates with the flour, beaten eggs, and panko breadcrumbs on them. Dredge each piece of chicken in the flour, then dip into the eggs, and finally into the panko breadcrumbs. Make sure to coat both sides evenly.
Meanwhile, heat the oil in a large skillet over medium high heat. Add the chicken one at a time, and cook, flipping once, until golden brown; about 4-5 minutes on each side. Transfer chicken to a baking rack or serving plate and sprinkle with flaky sea salt. Repeat with the remaining chicken breasts, adding more oil as needed.
Serve the chicken schnitzel with the fennel salad, shaved Pecorino Romano, and lemon wedges.
Enjoy!