Prepare the chicken. Slice the chicken breasts in half lengthwise to make thinner cutlets. Pat them dry, then season both sides with salt, black pepper, and garlic powder.
Dredge the chicken. Add the flour to a shallow plate. Lightly coat each piece of chicken on both sides, then shake off the extra flour.
Sear the chicken. Heat the olive oil in a large skillet over medium-high heat. Cook the chicken for 3 to 4 minutes per side, until golden brown and cooked through. Transfer the chicken to a plate.
Cook the mushrooms and onion. Add the butter to the same skillet, then add the mushrooms and onion. Cook for 6 to 8 minutes, stirring occasionally, until the onion softens and the mushrooms release their moisture, the liquid cooks off, and the mushrooms start to turn golden.
Add the garlic and flour. Stir in the garlic and cook for about 30 seconds, just until fragrant. Sprinkle 1 tablespoon flour over the mushrooms and stir for 30 to 45 seconds, until no dry flour remains.
Make the Marsala sauce. Pour in the Marsala wine first and let it bubble for about 1 minute while scraping the bottom of the skillet. Add the chicken broth and dried thyme, then simmer for 5 to 7 minutes, until the sauce is smooth, glossy, and lightly thickened.
Return the chicken. Add the chicken back to the skillet and spoon the mushroom Marsala sauce over the top. Simmer for 2 to 3 minutes, until the chicken is warmed through and coated in sauce.
Finish and serve. Stir in 1 tablespoon butter at the end for a smooth, glossy finish. Sprinkle with parsley if desired and serve warm.