Preheat the oven to 400°F (200°C).
Slice each large chicken breast in half lengthwise to make four thin cutlets. Pat dry with paper towels.
Season both sides of the cutlets with salt, pepper, and 1/2 teaspoon garlic powder, then dredge each piece lightly in flour, shaking off excess.
Heat 1 tablespoon olive oil and 1 tablespoon butter in an oven-proof skillet over medium-high heat until hot and shimmering.
Add the chicken cutlets and cook 4–5 minutes per side, until golden brown. Transfer the cooked chicken to a plate.
Add the remaining 2 tablespoons butter to the skillet and let it melt, then add the sliced cremini mushrooms.
Sauté the mushrooms, stirring occasionally, until browned, about 5–6 minutes.
Pour in 1/2 cup marsala and 1/4 cup chicken broth, scrape up any browned bits, and let the sauce bubble for about 1 minute.
Return the chicken to the skillet, spooning sauce and mushrooms over the cutlets, and cook 1 minute to heat through.
Remove the pan from heat, sprinkle 1 cup shredded mozzarella evenly over the chicken (concentrate on the cutlets), then sprinkle chopped scallions on top.
Place the skillet in the preheated oven and bake 7 minutes, until cheese is melted. Optionally broil 1–2 minutes to brown the cheese, watching closely.
Serve the chicken immediately, spooning extra pan sauce and mushrooms over each portion.