Place the chicken breasts side by side on a cutting board; cover them with plastic wrap and pound each breast until it is ¼ inch thick using a flat meat mallet (or rolling pin).
Mix the flour, salt, garlic powder, and pepper in a shallow bowl, dredge the chicken pieces in flour, and shake off any excess.
Heat 2 tablespoons of oil in a 12-inch pan or skillet over medium-high heat until shimmering. Fry three chicken breasts, turning once and carefully browning both sides (about 3 to 4 minutes per side). Transfer fried chicken cutlets to a plate covered with foil to keep them warm. Repeat the process for the remaining chicken breasts.
Place 1 tablespoon of butter in the same pan used to cook the chicken, and when it has melted, add mushrooms. Cook for 2 to 4 minutes until browned, scraping away at any leftover bits of chicken on the bottom. Season with salt and pepper if needed.
Stir in the thyme and minced garlic and cook until fragrant, about 1 minute.
Add the Marsala wine to the pan, then boil it down for a few seconds to allow the alcohol to dissipate.
Stir in the broth lower the heat, and simmer until reduced by half and starting to thicken (about 10-15 minutes).
Stir in the cream and the remaining one tablespoon of butter, and return the chicken breast back into the sauce. Simmer gently for bout 3 minutes or until the chicken is cooked through. (The sauce will continue to thicken when taken off the heat).
Adjust seasoning if desired. Garnish with chopped parsley and serve immediately.