To a large pan or skillet, add 2 Tbsp olive oil and 1 Tbsp butter and heat over MED-HIGH heat.
Sprinkle pounded chicken cutlets with salt and pepper on both sides, then lightly dredge in the 1/3 cup flour. Shake off excess flour and add chicken to hot pan. Work in batches if needed, as over-crowding the pan will prevent the chicken from crisping up.
Cook chicken about 3-4 minutes per side, until golden.
Transfer chicken to a plate and set aside.
Add 2 Tbsp olive oil and 1 Tbsp butter to the pan and add mushrooms.
Saute about 5-8 minutes, seasoning with salt and pepper about half-way through cooking.
Remove mushrooms to plate with the chicken and set aside.
Add remaining 1 Tbsp olive oil, then add shallots and garlic. Saute about 1 minute, until soft and fragrant.
Sprinkle in the 1 Tbsp flour and stir to coat. Cook for a minute to get the flour taste out.
Pour in Marsala wine and beef stock, scraping the bottom of the pan with a wooden spoon.
Cook, stirring often, for 2 minutes, or until sauce is slightly thickened.
Slide chicken and mushrooms back into the pan, making sure to get all the juices from the plate into the pan - that's pure flavor there!
Add 1 Tbsp butter to the center of the pan, toss a sprig of thyme in there if desired, then cover the pan and let cook about 2 minutes.
Stir and spoon sauce over chicken.
Garnish with parsley if desired and serve.