Cooked angel hair, for serving
- In a shallow bowl, season flour with salt and pepper. Dredge chicken in flour.
- In a large skillet over medium heat, melt 1 tablespoon butter and oil. Add chicken and cook until golden on both sides, about 5 minutes per side. Remove chicken from pan and place on a clean plate.
- Make marsala sauce: Melt remaining 1 tablespoon butter in skillet and add mushrooms. Cook until mushrooms are golden and liquid has been released, 6 to 8 minutes (if the pan looks dry, add a splash of olive oil). Add garlic and cook until fragrant, then season with salt.
- Add marsala, chicken broth, heavy cream, and parsley and bring to a simmer.
- Return chicken to skillet and spoon sauce over breasts. Simmer until chicken is cooked through, about 10 minutes.
- Serve over angel hair, if desired.