Heat a large cast-iron skillet over medium-high. Add the oil, four turns of the pan. When the oil ripples, add the mushrooms. Cook, stirring often, until the mushrooms brown, about 10 minutes. Season with salt and pepper. Add the thyme and garlic; toss 1 to 2 minutes. Add the marsala; cook, stirring often, until the liquid reduces by about two-thirds, about 4 minutes. Add the butter to the pan and swirl until blended. Discard the garlic and stir in the parsley.