Start by flattening the chicken breasts. This ensures even cooking. Season the flour with salt, garlic powder, and pepper. Dredge each piece of chicken in the seasoned flour, shaking off any excess.
Heat the butter and olive oil in a large skillet over medium heat. Add the chicken in batches, making sure not to overcrowd the pan. Sear until golden brown on both sides, about 4-5 minutes per side. Remove from the skillet and set aside.
In the same skillet, add butter, then the sliced mushrooms and shallots. Sauté until browned, about 5 minutes. Stir in the garlic and cook for an additional minute.
Sprinkle the flour over the mushroom mixture, stirring constantly for about two minutes. Gradually pour in the Marsala wine, scraping the bottom of the skillet to release any browned bits. Allow it to simmer.
Once the wine has cooked down a bit, add chicken broth and let it reduce slightly. Finally, stir in heavy cream along with the salt and pepper. Cook until the sauce thickens.
Return the chicken to the skillet, coating each piece thoroughly in the sauce. Cook on low heat for about 5 minutes until warmed through.
Garnish the dish with fresh parsley and serve hot over pasta or with crusty bread to soak up that delicious sauce.