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1. Adjust oven rack to lower-middle position, place large heatproof dinner plate on oven rack, and heat oven to 200 degrees. Heat 12-inch heavy-bottomed skillet over medium-high heat until very hot (you can hold your hand 2 inches above pan surface for 3 to 4 seconds), about 3 minutes. Pat chicken breasts dry. Meanwhile, place flour in shallow baking dish or pie plate. Season both sides of chicken cutlets with salt and pepper; working one piece at a time, coat both sides with flour. Lift breast from tapered end and shake to remove excess flour; set aside. Add oil to hot skillet and heat until shimmering. Place floured cutlets in single layer in skillet and cook until golden brown, about 3 minutes. Using tongs, flip cutlets and cook on second side until golden brown and meat feels firm when pressed with finger, about 3 minutes longer. Transfer chicken to heated plate and return plate to oven.
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2. Return skillet to low heat and add pancetta; saute, stirring occasionally and scraping pan bottom to loosen browned bits until pancetta is brown and crisp, about 4 minutes. With slotted spoon, transfer pancetta to paper towel--lined plate. Add mushrooms and increase heat to medium-high; saute, stirring occasionally and scraping pan bottom, until liquid released by mushrooms evaporates and mushrooms begin to brown, about 8 minutes. Add garlic, tomato paste, and cooked pancetta; saute while stirring until tomato paste begins to brown, about 1 minute. Off heat, add Marsala; return pan to high heat and simmer vigorously, scraping browned bits from pan bottom, until sauce is slightly syrupy and reduced to about 1 1/4 cups, about 5 minutes. Off heat, add lemon juice and any accumulated juices from chicken; whisk in butter 1 tablespoon at a time. Season to taste with salt and pepper, and stir in parsley. Pour sauce over chicken and serve immediately.
