Place the chicken breasts in the bottom of the slow cooker. Add the sliced mushrooms, diced onion, and minced garlic on top.
Sprinkle the fresh thyme leaves over the mushrooms and chicken. Pour the chicken broth around the ingredients.
Cover and cook on low for 5 to 6 hours until the chicken reaches an internal temperature of 165°F.
About 30 minutes before serving, place the cubed potatoes in a large pot and cover with water. Bring to a boil and cook until the potatoes are fork-tender.
Drain the potatoes and return them to the pot. Add the butter, milk, salt, and black pepper. Mash until smooth.
Serve the chicken breasts and mushrooms over or alongside the mashed potatoes. Spoon some of the cooking broth over each plate.