Season chicken with salt and pepper. Spread flour on a sheet of waxed paper; dredge chicken with flour on both sides, then gently shake off excess flour.
Heat 1 tablespoon of the butter in a heavy 12-inch skillet over medium-high heat until it starts to lightly brown and smell fragrant, then add olive oil, swirling pan to combine. Add chicken, skin side down, and sauté 3 minutes or until skin is lightly browned. Turn chicken and sauté second side 3 minutes; remove chicken, skin side up, to a plate.
Lower heat to medium and add another 1 tablespoon butter to skillet with shallots; sauté 2 minutes. Add mushrooms to skillet, raise the heat to high, and sauté until mushrooms are lightly browned and softened, about 2 to 3 minutes.
Pour in Marsala wine and let it boil 30 seconds, then add chicken stock. Place chicken breasts, skin side up, on top of mixture and continue to simmer 2 to 3 minutes, or until chicken is just barely pink in thickest parts when slit with a knife. Stir in parsley; season to taste with salt and freshly ground pepper.