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1
Heat the oven to 200u00b0F. Put the flour on a plate or in a shallow bowl next to the stove. If necessary, put each cutlet between 2 sheets of sheet of plastic wrap and pound to uniform thickness; blot the chicken dry with a paper towel and sprinkle with salt and pepper.
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2
Put the oil and 2 tablespoons of the butter in a large skillet over medium-high heat. When the butter has melted, turn a piece of the chicken in the flour to coat it on all sides; shake off any excess. Add the floured chicken to the pan, then repeat with the next piece; work in batches if necessary to avoid crowding the pan.
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3
Cook, adjusting the heat as needed so that the fat is always bubbling but the chicken doesn't burn. After 2 minutes, rotate the chicken so that the outside edges are moved toward the center and vice versa (don't flip them; you want the same side in contact with the fat). When the bottom of each piece is brown, after 3 to 4 minutes, turn them over.
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4
Cook on the second side, adjusting the heat as described in Step 3, until the chicken is firm to the touch but still a bit pink inside, another 3 to 4 minutes. To check for doneness, cut into a piece with a thin-bladed knife and take a peek. Transfer the chicken to an ovenproof platter and put it in the oven.
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5
Add the wine to the skillet, keeping the heat at medium-high. Let it bubble away as you stir and scrape the bottom of the pan, until about half the wine has evaporated, a minute or two. Pour in the water and continue to stir until the liquid has thickened slightly and reduced to 1/4 cup, another 2 or 3 minutes. Add the remaining tablespoon of butter to the skillet and swirl the pan around until the butter melts; turn off the heat.
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6
Remove the chicken from the oven, and if any juices have accumulated on the platter, add them to the skillet along with the 1/4 cup parsley. Stir, taste the sauce, and adjust the seasoning. Spoon the sauce over the chicken, garnish with the remaining 2 tablespoons parsley, and serve with the lemon quarters.
