Start by seasonings the chicken breasts with salt and pepper. Heat the olive oil in a skillet over medium-high heat until shimmering, then add the chicken and sear for about 3-4 minutes per side until golden brown. Remove and set aside.
In the same skillet, add sliced mushrooms and cook until they release their moisture and turn brown, about 5-7 minutes. Stir occasionally to develop a deep earthy aroma and even browning.
Pour in the Marsala wine, scraping up any browned bits from the bottom of the skillet. Bring the wine to a simmer and cook until it reduces by half, about 3-4 minutes, intensifying its rich, sweet aroma.
Transfer the seared chicken breasts to the crockpot. Pour the mushroom and wine mixture over the chicken, then add the sliced onion, minced garlic, dried thyme, and chicken broth. Toss in a pinch of salt and pepper for seasoning.
Cover the crockpot and cook on low for 4-6 hours, until the chicken is tender and easily shreddable. The aroma of wine and mushrooms will fill your kitchen as it slowly develops deep, savory flavors.
Once cooked, remove the chicken and mushrooms from the crockpot. Turn the crockpot to high if you'd like to thicken the sauce, and stir in the butter until melted and glossy, about 2 minutes.
Taste the sauce and adjust seasoning with more salt or pepper if needed. Return the chicken and mushrooms to the sauce briefly to rewarm and coat with the glossy sauce.
Garnish with freshly chopped parsley for a fresh pop of color and flavor. Serve hot over pasta or mashed potatoes, spooning the rich, mushroomy sauce over the top.