Melt the butter with the oil in the same pan over medium-high heat. Add the mushrooms & cook, without stirring for 2 to 3 minutes until mushrooms are seared. Toss & continue to cook for a further 2 to 3 minutes until browned & cooked. Add the shallot & garlic. Cook, stirring, for 2 minutes until fragrant & the shallot is beginning to soften.
Add the marsala & cook, uncovered, until the reduced by half. Add the broth, cream, nutmeg, salt & pepper. Turn heat to medium-low & simmer, uncovered, about 2 minutes until the sauce starts to thicken.
Add the chicken back into the pan, turning to coat. Let the chicken warm for 1 to 2 minutes & the sauce becomes your designed consistency; sprinkle with extra thyme. Serve with sides of your choice. Serves 4.