The bracing acidity from the lemons and bright brininess of the olives and capers makes this a standout dish. It's perfect for a casual weeknight dinner but special enough to serve for any occasion.
Squeeze the juice from 1½ of the lemons and reserve. Lay the remaining lemon half flat side down and cut into very thin slices with a paring knife. Remove pits and set the lemon slices aside.2.
Season the scaloppini with salt and pepper. Dredge in flour to coat both sides lightly and tap off excess flour. Heat 3 tablespoons of olive oil and 2 tablespoons of butter in a wide, heavy skillet over medium heat until butter is foaming. Add as many of the scaloppini as will fit without touching and cook until golden-brown on the underside, about 3 minutes. Flip and cook until the second side is lightly browned, about 2 minutes. Remove and drain on paper towels. Repeat with remaining scaloppini.3.
Remove all scaloppini from the pan. Pour off the fat and carefully wipe out the skillet with a wad of paper towels. Pour in the remaining 3 tablespoons olive oil and add the remaining 4 tablespoons butter, the garlic and lemon slices. Cook, scraping the bottom of the skillet, until the garlic is golden-brown, about 3 minutes. Scoop out lemon slices and set aside. Scatter the olives and capers into the skillet and cook, stirring gently, until they begin to sizzle, about 4 minutes. Pour in the wine, bring to a vigorous boil and cook until reduced in volume by half. Pour in the chicken stock, bring to a boil and cook until slightly syrupy, about 4 minutes.4.
Return the scaloppini to the skillet, turning the cutlets in the sauce until they are cooked through and coated with sauce. Swirl in the parsley and divide the scaloppini among warm plates. Spoon sauce over them and decorate with reserved lemon slices. Serve over braised spinach.