In a shallow dish, whisk together the all-purpose flour, salt, and black pepper.

Dredge each chicken cutlet in the flour mixture, shaking off the excess to ensure a thin, even coating.

In a large heavy-bottomed skillet over medium-high heat, melt 2 tablespoons of butter with the olive oil.

Add the chicken to the skillet in batches, searing for 3 to 4 minutes per side until golden brown and cooked through. Transfer chicken to a warm plate and set aside.

In the same skillet, melt the remaining 2 tablespoons of butter. Add the sliced mushrooms and sauté for 8 to 10 minutes until browned and the released moisture has evaporated.

Stir in the minced shallot and garlic, cooking for 1 to 2 minutes until fragrant and softened.

Pour in the dry Marsala wine, using a wooden spoon to scrape the bottom of the pan to release the browned bits (fond). Simmer until the wine has reduced by half.

Whisk in the chicken stock and heavy cream. Bring to a gentle simmer and cook for 5 to 7 minutes until the sauce has thickened to a silky consistency.

Return the seared chicken and any accumulated juices to the skillet. Simmer for an additional 2 to 3 minutes to allow the flavors to meld and the chicken to heat through.

Garnish with fresh parsley and serve immediately over pasta, polenta, or mashed potatoes.