For the Chicken Paillard with Garlicky Greens:
4 pieces boneless, skinless chicken breasts, no tenders attached, butterflied open and pounded in plastic bags or between plastic film to no more than ⅛-inch thick
Salt and pepper
4 tablespoons extra-virgin olive oil (EVOO)
2 large cloves garlic, chopped or grated or thinly sliced
1 bunch rainbow Swiss chard or 1 pound spinach, stemmed
For the Mornay Sauce:
3 tablespoons butter
3 tablespoons flour
1½ cups milk
Freshly grated nutmeg, a few grates or to taste
Salt and white pepper or fine black
½ cup freshly grated Parmigiano-Reggiano cheese
For the Frico Eggs:
1½ cups freshly grated Parmigiano-Reggiano cheese
4 large cage-free eggs
Salt and pepper
For the chicken, heat a large cast-iron skillet over medium-high heat. Season chicken with salt and pepper.
For the mornay sauce, heat a saucepot over medium to medium-high heat. Melt butter, whisk in flour, whisk in milk, bring to bubble and season with salt and white or fine black pepper, a few grates of nutmeg. Thicken to just coat spoon and stir in cheese, then reduce heat to low.
Add EVOO, 2 turns of the pan, to cast-iron skillet and cook chicken 2 at a time to brown on both sides and cooked through, about 4 minutes for each set. Keep warm on covered platter.
For the greens, heat a nonstick skillet with EVOO, 2 turns of the pan, over medium heat, add garlic, wilt in greens and season lightly with salt and pepper. Add juice of 1 lemon and turn off heat.
For eggs, use a small nonstick skillet or 2 if you have them. Heat skillet over medium heat with a generous handful of parm, enough to coat the bottom. When it begins to melt, top with egg and cover with lid or foil. Cook to desired doneness and season with salt and pepper. Let eggs stand 2 minutes to remove so the cheese sets.
Build plates: chicken paillard in pool of sauce or topped with some sauce, greens, frico egg, serve.