Pound chicken to 1/4" thick (you can cut them in half if they're very large). Season with salt and pepper and dredge in flour.
Preheat olive oil in a large pan over medium high heat. Cook chicken in batches, 3-4 minutes per side or until cooked through. Remove chicken and place on a plate.
In the same pan, add 2 tablespoons butter, thyme and shallot. Cook until tender, about 3 minutes. Add mushrooms and cook until juices are released, about 5 minutes. Stir in flour 1 1/2 tablespoons flour and cook 1 minute more.
Add Marsala wine and broth and simmer about 3 minutes, until thickened and bubbly.
Place chicken back into the pan and simmer 2-3 minutes or until hot.
(Nutrition information provided is an estimate and will vary based on cooking methods and brands of ingredients used.)