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Heat a large skillet over medium heat. Cook bacon, stirring frequently, until fully cooked, about 7 minutes. Remove with a slotted spoon to a paper-towel lined plate.
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Season chicken with salt and pepper and dredge in flour. (Discard excess flour.) Place chicken in the skillet with bacon fat in a single layer. (Cook chicken in 2 batches if it doesn’t fit.) Cook over medium high heat for 3-4 minutes per side, until chicken is cooked through (internal temperature of 165 degrees). Remove chicken to a plate.
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In the same skillet, melt butter over medium heat. Add mushrooms and season with salt and pepper. Cook, stirring occasionally, until mushrooms release their juices, about 8 minutes. Add garlic and cook 1-2 more minutes, until fragrant.
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Pour in marsala wine and scrape any browned bits off the bottom of the skillet. Pour in chicken broth. Let simmer for 15 minutes, so sauce is slightly reduced.
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Add mascarpone cheese and stir until cheese is melted and incorporated into the sauce. Stir bacon pieces into the sauce. Nestle chicken back into the mushroom sauce and cook 3-5 more minutes, until heated through. Garnish with chopped parsley.