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.
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.
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.
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.
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.