Prep the chicken. If using large chicken breasts, place one on a large cutting board and slice through it horizontally with a sharp knife to yield two cutlets. Cut the remaining breasts the same way.

Dredge the chicken. Season both sides of the cutlets with the salt and pepper. Working with one cutlet at a time, dip it in the flour, taking care to coat it on all sides. Shake off the excess flour and set aside. Repeat with remaining cutlets. Measure three tablespoons of the remaining flour and discard the rest.

Sear the chicken. Heat a large, heavy-bottomed sauté or frying pan over medium-high heat. Add the olive oil and the butter. When the oil and butter are hot and the butter is beginning to brown, lay 2 or 3 in the pan—as many as will fit comfortably without crowding. Cook for 3 to 4 minutes, until browned on the bottom, then carefully turn them over with tongs and brown the other side, another 3 to 4 minutes. The cutlets should be golden and not too dark. If they are browning too quickly, turn down the heat. Once browned, transfer the cutlets to a plate. Repeat with the remaining cutlets, adding 1 or 2 tablespoons more olive oil between batches if needed. The chicken does not have to be completely cooked through at this point.

Deglaze with the mushrooms. Once all cutlets have been browned, add the mushrooms to the pan and spread them into an even layer. Cook, without stirring, until they sizzle and release their liquid, about 3 minutes. Stir the mushrooms and scrape the pan with a wooden spoon to release the browned bits clinging to the pan.

Sear the mushrooms. Increase heat to medium-high and cook, without stirring, until all liquid evaporates and mushrooms have slumped completely begin to caramelize, about 4 minutes. Stir again, spread into an even layer again and sear, without stirring, another 2 minutes. Add the garlic and stir to combine, until fragrant.

Make the marsala sauce. Sprinkle 3 tablespoons of flour left over from dredging chicken, garlic powder, and onion powder over the mushrooms and stir until the flour toasts lightly and smells nutty and aromatic, about 1 minute. Increase heat to high. Add the marsala and cook, stirring, until almost completely evaporated, 2 minutes. Pour in the chicken stock, milk, and cream and bring to a boil. Lower heat to medium-low and simmer vigorously, swirling pan occasionally to redistribute mushrooms, until slightly thickened and mixture coats the back of a spoon, about 5 minutes. Taste sauce and adjust seasoning with additional salt and pepper.

Finish and serve. Nestle chicken breasts back into the pan, along with any accumulated juices. Spoon the sauce over top and simmer, uncovered, until the chicken is cooked through. Sprinkle with fresh parsley and serve.