Begin by pounding the chicken breasts to an even 1.5 cm (½ inch) thickness, then season them generously with salt and pepper. Lightly dredge each piece in flour, shaking off the excess, and set aside.
Heat a tablespoon of olive oil in a large skillet over medium-high heat until shimmering. Add the chicken and sear for about 3-4 minutes per side until golden brown and cooked through. Remove the chicken from the pan and tent with foil to keep warm.
In the same skillet, add a tablespoon of butter and sliced mushrooms. Sauté until the mushrooms are deeply golden and fragrant, about 5 minutes, stirring occasionally. The mushrooms should develop a rich aroma and a slight caramel color.
Push the mushrooms to one side of the pan and add the minced garlic to the cleared space. Cook for about 30 seconds until fragrant, being careful not to burn it. Mix the garlic into the mushrooms.
Pour the semi-sweet Marsala wine into the skillet, scraping up any browned bits from the bottom. Bring to a gentle simmer and cook until the wine has reduced by half, about 3 minutes, until the mixture is syrupy and aromatic.
Stir in the remaining butter to enrich the sauce, creating a glossy, velvety consistency. Taste and adjust seasoning with salt and pepper as needed.
Return the seared chicken breasts to the skillet, spooning sauce and mushrooms over them. Cook for an additional 2-3 minutes to reheat and allow flavors to meld. The sauce should coat the chicken with a shiny, rich glaze.
Transfer the chicken to serving plates, spooning generous amounts of the mushroom sauce over each piece. Garnish with chopped parsley for a fresh contrast. Serve immediately to enjoy the tender chicken and flavorful sauce.