Place the cutlets between two sheets of plastic wrap and pound to an even 0.5 inch thickness; pat dry with paper towels.
In a shallow dish, whisk the all-purpose flour, kosher salt, and black pepper together. Dredge each cutlet in the seasoned flour, shaking off excess.
Heat the olive oil in a large skillet over medium-high heat until shimmering. Sear the boneless skinless chicken breast cutlets until golden, 3β4 minutes per side, just cooked through (155β160Β°F in the center). Transfer to a warm plate and tent loosely with foil.
Reduce heat to medium and add the 1 tablespoon unsalted butter to the skillet. Add the cremini mushrooms and cook, stirring occasionally, until browned and their liquid evaporates, 6β8 minutes. Stir in the shallot and garlic and cook until fragrant, 1β2 minutes.
Pour in the dry Marsala wine, scraping up browned bits, and simmer until reduced and slightly syrupy, 2β3 minutes.
Add the low-sodium chicken stock and simmer until the sauce is reduced by about half and lightly coats the back of a spoon, 5β7 minutes.
Return the chicken and any accumulated juices to the pan, turning to coat, and simmer until warmed through and the sauce clings to the cutlets, 2β3 minutes. Off the heat, swirl in the 2 tablespoons unsalted butter until glossy. Sprinkle with fresh parsley and serve immediately.