Lay the chicken thighs between two pieces of plastic wrap and pound to 1/2 to 3/4 inches thick with a mallet. Set up 3 medium bowls: fill one with the flour mixed with the salt and pepper; fill the second with the eggs; spread the breadcrumbs in the third.
Dip the chicken thighs in the flour, coating them evenly. Next, dip in the egg wash, coating so no flour shows underneath. Finally, dip in the breadcrumbs, making sure the thighs are evenly covered.
Heat the oil in a 12-inch skillet to about 350 degrees F. Fry the chicken until golden brown on both sides and cooked through, about 3 minutes per side. Drain on paper towels and set aside.
For the sauce: Roughly chop the garlic and small-dice the shallot, then throw them into the skillet to sauté. As soon as the garlic and shallots start to color, deglaze the pan with the white wine and cook for 1 minute. Add the chicken stock and reduce by half. Over low heat, whisk in the olive oil and butter to thicken the sauce. Add the capers, parsley and the juice of 1 lemon. Transfer the sauce to a container and set aside.
Halve the other 2 lemons and sear them in the skillet, cut-side down, until caramelized.
Whisk together the olive oil, lemon juice, Dijon, salt and pepper. Toss with the frisee.
Place the crispy chicken on plates, cover with lemon-caper sauce, top with frisee salad and garnish with a burnt lemon half. Sprinkle with chervil, tarragon, parsley and a generous amount of Parmesan.