Season chicken with ½ teaspoon of salt and pepper, then dredge in flour and shake off any excess.
In a large skillet, heat olive oil and melt 1 tablespoon of butter on medium heat. Swirl pan to coat with oil and butter evenly.
Brown the chicken (do not overcrowd and work in batches if needed) for 4-5 minutes on each side or until golden brown and cooked through. Transfer onto a plate, cover, and set aside
In the same skillet, melt the remaining butter, add the mushrooms and season with ½ teaspoon salt, cook and stir regularly for 3 minutes.
Add the garlic and saute for a minute or until it's fragrant. Add the marsala wine, and deglaze the pan scraping any bits stuck to the bottom of the pan with a wooden spoon. Simmer and reduce the wine by half.
Adjust the heat to medium-low, and add the heavy cream to the skillet. Allow the sauce to simmer for a couple of minutes.
Return the chicken to the sauce to rewarm it, cook for 1 more minute then remove from heat. Garnish with fresh parsley if desired, and serve.