Place each chicken breast half between 2 sheets of heavy-duty plastic wrap; pound to 1/2-inch thickness using a meat mallet or rolling pin. Sprinkle chicken with salt, pepper, and flour.
Heat 1 tablespoon butter in a large nonstick skillet over medium heat. Add chicken; cook 5 minutes on each side or until done. Remove chicken from pan; keep warm. Add mushrooms and shallots to pan; sauté 5 minutes or until tender. Stir in wine, scraping pan to loosen browned bits; add stock. Bring to a boil; cook until reduced to 1 cup (about 10 minutes). Cut remaining 1 tablespoon butter into small pieces. Remove pan from heat. Add butter, stirring until butter melts. Spoon sauce over chicken. Sprinkle with parsley.