Preheat the oven to 400 degrees F.
Simmer the garlic in a saucepan of water until tender, about 10 minutes (this will soften the flavor). Drain and let cool, then pop the jackets off the cloves and reserve.
Sprinkle the chicken with salt and pepper. Heat the EVOO in a large ovenproof skillet. Add the chicken, skin-side down, and cook until the skin is browned and very crisp, 7 to 8 minutes. Flip the chicken and brown the other side, 3 to 4 minutes more. Remove the chicken to a plate. Melt the butter into the fat remaining in the skillet and add the mushrooms and thyme. Cook until the mushrooms are browned and very tender, 12 to 15 minutes. Deglaze with the Marsala, stirring and scraping up any browned bits from the bottom of the skillet with a wooden spoon. Return the chicken to the skillet, skin-side up, and add the garlic. Add enough stock to come up and around the chicken but not cover the skin. Transfer the skillet to the oven and cook for 45 minutes.
Transfer the chicken to a warmed platter and loosely tent with foil. Reduce the sauce on the stovetop until it is thick enough to coat the back of a spoon. Add the kale and cook until just wilted, then stir in a bit of nutmeg.
Spoon the sauce and kale into shallow bowls and top with the chicken. Serve with warm bread for mopping.
You can make the chicken and sauce ahead of time. Remove the chicken from the skillet to keep the skin crisp and transfer the sauce to a casserole dish. Lay the chicken in the sauce, making sure the skin is not covered. Refrigerate until ready to serve. To reheat, bring the sauce to a simmer in a skillet, then add the chicken. Transfer to a 400 degree F oven to heat through and re-crisp the skin. Warm a platter on a low oven rack for 2 minutes and crisp the bread. Transfer the warm chicken to the platter and loosely tent with foil. Reduce the sauce on the stovetop, add the kale and nutmeg and serve with the bread.