If using 2 large chicken breasts, slice them in half horizontally to get 4 chicken cutlets. Place the chicken breasts between 2 pieces of plastic wrap or parchment paper and pound to ¼-inch thickness using a meat mallet or rolling pin.
Sprinkle both sides of the chicken breasts with salt and pepper.
Place the flour in a shallow bowl or baking dish. Coat each piece of chicken with the flour, gently shaking off any excess flour.
Heat the olive oil in a large skillet over medium heat. Once hot, add the chicken to the pan and brown on both sides, about 5-6 minutes per side, until the chicken is cooked through to 165° F. Remove chicken to a clean plate. If desired, tent with foil to keep warm.
Add the butter and cremini mushrooms to the pan and cook, stirring often, until softened and golden brown, 3-4 minutes. Add the garlic and cook, stirring, for 30 seconds.
Stir in the Marsala wine, chicken broth and thyme. Simmer, stirring often, until the sauce reduces by almost half, about 3-4 minutes. (The sauce will thicken up more when you add the chicken back to the pan because of the flour on the chicken.)
Return the chicken to the pan for about 2 minutes to warm through. Serve chicken with sauce, over mashed potatoes, pasta, polenta, or as desired.