Place chicken breasts between plastic wrap and pound to an even 1/2-inch thickness using a meat mallet or rolling pin. In a shallow bowl, whisk together the flour, garlic powder, onion powder, Italian seasoning, 1 tsp salt, and 1/2 tsp black pepper.
Pat each chicken breast completely dry with paper towels, then dredge in the seasoned flour mixture, pressing gently to adhere on all sides. Shake off any excess flour.
Heat a large skillet over medium-high heat, add olive oil, and sear chicken for 4–5 minutes per side until deep golden brown and the internal temperature reads 165°F (74°C). Transfer to a plate and tent loosely with foil.
Reduce heat to medium and melt butter in the same skillet. Add sliced mushrooms in a single layer and cook undisturbed for 2–3 minutes, then stir and cook another 2–3 minutes until golden and any liquid has evaporated.
Add minced garlic to the mushrooms and stir constantly for about 30 seconds until fragrant, being careful not to let it burn.
Pour in the dry Marsala wine and use a wooden spoon to scrape up all the browned bits from the bottom of the pan. Simmer for 3–4 minutes, stirring occasionally, until reduced by about half and the sauce turns a deep amber color.
Stir in the chicken broth and simmer 2 minutes, then reduce heat to medium-low and slowly pour in the heavy cream while stirring. Add the thyme and simmer gently for 4–5 minutes until the sauce coats the back of a spoon.
Nestle the seared chicken breasts back into the sauce and spoon sauce over each piece. Simmer on low for 3–4 minutes until the chicken is warmed through and has absorbed some of the sauce flavor.
Remove from heat, sprinkle with fresh chopped parsley, and serve immediately over buttered pasta, mashed potatoes, or rice with extra sauce spooned generously over the top.