Flatten the chicken breasts slightly by pounding them to even thickness.
Sprinkle both sides with salt and pepper, then coat with flour.
Heat olive oil in a large skillet over medium heat.
Add chicken breasts and cook until golden brown on each side, about 3-4 minutes per side.
Remove chicken from the skillet and set aside.
Melt butter in the same skillet.
Add mushrooms, shallots, and garlic, cooking until mushrooms are tender.
Pour in Marsala wine and chicken broth, scraping up any browned bits from the pan's bottom.
Bring to a simmer and reduce for a few minutes until the sauce thickens slightly.
Stir in heavy cream, then return the chicken to the skillet.
Cook for another 5-7 minutes until the chicken is cooked through and sauce is thickened.
Serve over pasta or mashed potatoes for a full meal.