Butterfly each chicken breast by slicing horizontally through the thickest part, opening it like a book. Place between two sheets of plastic wrap and pound with a meat mallet or the bottom of a heavy skillet until evenly ½ inch thick. Uniform thickness is the difference between evenly cooked and half-raw chicken. Season both sides with salt and pepper.
Mix the flour, garlic powder, salt, and pepper in a shallow dish. Dredge each cutlet in the seasoned flour, shaking off the excess — you want a thin, even coating, not clumps. Set on a wire rack while you prep the rest. The brief rest helps the flour adhere during cooking.
Heat a large 12-inch skillet over medium-high heat. Add the torn prosciutto pieces in a single layer and cook for 2-3 minutes per side until crispy and curled like bacon chips. Remove to a paper towel-lined plate. Do not wipe the pan — the rendered prosciutto fat is flavor.
Add the olive oil and 2 tbsp butter to the same skillet with the prosciutto fat. When the butter foams and the foam subsides, lay in the chicken cutlets. Do not crowd — work in two batches if needed. Cook for 3-4 minutes per side until golden brown and cooked through (internal temp 165°F). Transfer to a clean plate and tent loosely with foil. Do not cut into the chicken to check — use a thermometer.
Reduce heat to medium. In the same skillet with all the fond, add the sliced mushrooms in a single layer. Let them cook undisturbed for 3-4 minutes until they release their liquid and develop golden-brown edges. Stir and cook another 2 minutes. Resist the urge to stir constantly — mushrooms need contact with the hot pan to brown, not steam.
Add the minced shallots and garlic to the mushrooms and cook for 60 seconds until fragrant. Push everything to the edges of the pan.
Remove the pan from the heat and pour in the dry Marsala wine — pulling the pan off the burner first prevents any flare-up. Return to heat and stir, scraping up every bit of fond from the bottom. Let the wine reduce by half, about 2-3 minutes. The kitchen will smell incredible.
Add the chicken stock and bring to a steady simmer. Cook for 5-6 minutes until reduced by about a third and the sauce starts to look slightly syrupy. Add the heavy cream and simmer for another 2-3 minutes until the sauce coats the back of a spoon and leaves a clear trail when you drag your finger through it.
Remove from heat. Swirl in the 2 tbsp cold butter and the lemon juice — the butter adds body and gloss, the lemon juice cuts through the richness and wakes everything up. Taste and adjust salt. This is the step most recipes skip and it's the difference between good and restaurant-grade.
Nestle the chicken cutlets back into the sauce, spooning it over the top. Let them warm through for 60 seconds. Plate each cutlet with a generous ladle of mushroom sauce, top with crispy prosciutto pieces, and finish with chopped fresh parsley and a crack of flaky sea salt. Serve immediately with crusty bread for soaking up the sauce — non-negotiable.