Preheat oven to 350°.
Sprinkle chicken evenly with 1/4 teaspoon salt, 1/4 teaspoon pepper, and grated nutmeg. Place chicken in a shallow roasting pan coated with cooking spray; cover with foil. Bake chicken, covered, at 350° for 30 minutes. Turn chicken over; bake, uncovered, an additional 30 minutes or until chicken is done. Remove chicken to a serving platter, reserving 1 tablespoon of pan drippings. Keep chicken warm.
Place potatoes in a medium saucepan; cover with water. Bring to a boil; cook 15 minutes or until very tender. Drain. Return potatoes to pan; add milk, 1 tablespoon butter, remaining 1/4 teaspoon salt, and remaining 1/4 teaspoon pepper; mash with a potato masher to desired consistency.
Heat reserved pan drippings in a large skillet over medium heat. Add mushrooms to pan; cook 3 minutes or until moisture evaporates, stirring constantly. Stir in broth and wine, scraping pan to loosen browned bits; cook 5 minutes, stirring frequently. Remove from heat; stir in remaining 1 tablespoon butter. Drizzle gravy over chicken; sprinkle with parsley. Serve with potatoes.