Begin by seasoning the halved chicken breasts with salt, pepper, and garlic powder on both sides.
Lightly dredge each piece of chicken in flour, shaking off any excess.
In a large skillet, heat the olive oil and 1 tablespoon of butter over medium heat.
Add the floured chicken breasts to the skillet and cook for about 4-5 minutes on each side or until golden brown and cooked through. Remove the chicken from the skillet and set aside.
In the same skillet, add the remaining 2 tablespoons of butter. Once melted, add the sliced cremini mushrooms. Season with a bit of salt and pepper, then sauté until they are tender and browned, about 5-7 minutes.
Pour in the Marsala wine and chicken broth, scraping up any browned bits from the bottom of the skillet. Allow the sauce to simmer for a few minutes until slightly reduced.
Return the cooked chicken to the skillet, spooning some of the sauce over the top. Sprinkle the shredded mozzarella evenly over the chicken, then cover the skillet with a lid and let it cook for another 2-3 minutes, or until the cheese is melted.
Once the cheese is gooey and melted, remove the skillet from the heat. Garnish with chopped scallions before serving.