Season the chicken thighs generously with salt and pepper. Heat the olive oil in a large skillet over medium heat until shimmering, then brown the chicken for about 3-4 minutes per side until golden brown. Transfer the browned chicken to the slow cooker.
In the same skillet, add the chopped garlic and sliced mushrooms. Sauté for about 5 minutes until the mushrooms are deeply browned and fragrant, and the garlic is fragrant. Pour in a splash of Marsala wine, scraping up any browned bits, then transfer everything to the slow cooker.
Pour the remaining Marsala wine and chicken broth into the slow cooker. Gently stir to combine, making sure the chicken is coated with the sauce. Cover and set the slow cooker to low for 6 hours, avoiding lifting the lid during the first 4 hours to keep flavors concentrated.
Once cooking time is up, open the lid and check that the chicken is fork-tender and mushrooms are soft. If the sauce appears thin, turn the slow cooker to high and simmer uncovered for 15-20 minutes to thicken, stirring occasionally.
Add a pat of butter to the sauce and stir until glossy and silky. Taste and adjust seasoning with salt and pepper as needed. Sprinkle freshly chopped parsley over the top for a fresh herbal note.
Serve the chicken thighs with generous spoonfuls of the mushroom and Marsala sauce over pasta, rice, or crusty bread. Enjoy the rich, tender chicken with the glossy, flavorful sauce that tastes like it simmered all day.