Spread flour in shallow dish. Pound thicker ends of the chicken breasts as needed. Pat dry with paper towel, season with salt and pepper. Dredge through the flour to coat, shake off any excess.
Heat 2 tablespoons of oil into a 12" skillet over medium-high heat until just smoking. Add the chicken and cook until golden brown on both sides, about 10 minutes. Transfer chicken to plate.
Add remaining 1 tablespoon of oil to the skillet and return to medium-high heat until shimmering. Add the pancetta and mushrooms. Cook until pancetta is crisp and mushrooms are brown, about 10 minutes.
Stir in garlic and tomato paste. Cook until the tomato paste begins to brown, 1 minute. Stir in Marsala, scraping up any browned bits, and simmer until reduced and slightly syrupy, about 8 minutes.
Stir in lemon juice and any accumulated chicken juice. Turn heat to low and whisk in butter, one piece at a time. Off heat, stir in parsley and season with salt and pepper. Spoon sauce over chicken before serving.
Recipe by the minimalist table at https://www.daraboxer.com/theminimalisttable/chicken-marsala/