Clean the mushrooms and cut them into thick slices. (See Tips & Tricks for mushroom cleaning ideas.) You can use the stems, but trim off the very bottom.
Melt the butter in a large skillet over medium high heat.
Add the mushrooms to the skillet. Sprinkle the garlic powder over the mushrooms and lightly salt.
Stir the mushrooms occasionally and cook until soft, about 4-5 minutes.
Add the fresh thyme leaves (remove them from the stem as much as possible) and cook until fragrant, about one minute.
Remove the mushrooms to a small bowl and set aside.
Heat the olive oil in the same skillet.
Carefully add the chicken pieces to the skillet. Cook for 4-5 minutes on each side until golden brown. The chicken will finish cooking in the sauce.
Return the mushrooms to the skillet.
Add the chicken broth and scrape up any browned bits from the bottom of the pan.
Carefully add the marsala cooking wine. I generally move it off the burner for a minute to avoid any flare up.
Pour in the heavy cream in a steady stream.
Stir everything together with wooden spoon or heat resistant spatula.
Use a ladle to remove about 1/4 cup of liquid. You can put it in the measuring cup you used for your liquids.
Add the all purpose flour to the liquid and whisk together (you can also combine it with a fork). Make sure it is fully incorporated.
Return the liquid to the skillet and lower to medium heat. Spoon the sauce over the chicken.
Allow the sauce to thicken and the chicken to cook through, about 8 minutes. The chicken is cooked when it is no longer pink inside and when an instant read thermometer reaches 165 degrees.
When the chicken is cooked and the sauce thickened, lightly salt and pepper. You can also sprinkle with a bit of shredded parmesan and/or snip some fresh parsley over the surface.