Butterfly the chicken breasts into cutlets by slicing horizontally through the middle.
Place the cutlets between plastic wrap and pound to an even thickness.
Season both sides of the chicken with 1 teaspoon salt and ½ teaspoon pepper (divided evenly).
Place ½ cup flour in a shallow dish and dredge the chicken, shaking off excess.
Heat ¼ cup olive oil in a large skillet over medium-high heat until shimmering.
Cook chicken for 3-4 minutes per side until golden brown, then transfer to a wire rack to rest.
If needed, wipe out any burnt bits from the pan, leaving the flavorful brown bits.
Add 2 tablespoons butter and 2 tablespoons olive oil to the pan over medium heat.
Add mushrooms, remaining ½ teaspoon salt, and remaining ½ teaspoon pepper.
Cook mushrooms until lightly browned, stirring occasionally, about 5-7 minutes.
Add garlic and stir constantly for about 1 minute until fragrant.
Sprinkle 1 tablespoon flour over the mushroom mixture and stir to coat.
Pour in the Marsala wine and stir, scraping up any brown bits from the bottom of the pan.
Add chicken stock and reduce heat to low. Let simmer until sauce begins to thicken, about 5 minutes.
Stir in heavy cream and mix well.
Return chicken to the pan and simmer on low heat for 2-4 minutes until warmed through.
Serve immediately over pasta if desired.