Working one at a time, place chicken on a cutting board; slice each in half horizontally to create four thin cutlets.
Sprinkle chicken evenly on both sides with 1½ teaspoons salt and ½ teaspoon pepper. Place in a shallow dish with flour; toss and pat to coat chicken with flour.
Heat ¼ cup olive oil over medium-high heat until shimmering. Add chicken to pan; cook until browned on both sides, 3 to 4 minutes per side. Place chicken on a wire rack to drain.
Wipe skillet clean, if needed. Reduce heat to medium. Add remaining 2 tablespoons oil and butter.
Add mushrooms; sprinkle with remaining ½ teaspoon each salt and pepper. Cook, stirring occasionally, until mushrooms are lightly browned, about 5 minutes.
Add garlic; cook, stirring often, about 1 minute.
Add flour; cook, stirring often, until flour is slightly toasted, about 1 minute.
Add marsala to pan; stir to release browned bits from bottom of pan. Add chicken stock.
Reduce heat to medium-low; simmer until slightly thickened, about 10 minutes.
Stir in cream; return chicken to pan. Cook until chicken is warmed through, about 2 minutes.
Remove from heat. Divide chicken and sauce among 4 plates. Sprinkle with parsley, and serve.
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Notes
Buying chicken cutlets at the grocery store is a big timesaver, and perfectly acceptable for this recipe. If doing so, aim for about 1¼ lbs chicken cutlets.
Be sure to get the oil nice and hot before adding the chicken. Cutlets cook very quickly, and the hotter the oil, the crispier your chicken will be.
If you’d like, you can place the wire rack with the cooked chicken on a rimmed baking sheet, and keep in warm in a 200°F oven while finishing the marsala sauce.
Marsala is a fortified Italian wine that is available in dry and sweet versions; the dry version is best for this recipe.
Any mushrooms will work in this recipe; use a wild mushroom blend for a gourmet twist.