1. Preheat oven to 450°.
2. Heat a large ovenproof skillet over high heat. Add 1 tablespoon oil. Sprinkle chicken with 1/4 teaspoon salt and pepper; add to pan. Cook 3 minutes or until browned. Turn chicken; place pan in oven. Bake at 450° for 9 minutes or until done. Remove chicken from pan; keep warm. Heat pan over medium-high heat. Add 1/2 cup broth and cider; bring to a boil, scraping pan to loosen browned bits. Reduce heat to medium-low; simmer 4 minutes or until thickened. Whisk in mustard, 1 tablespoon butter, and parsley.
3. Heat remaining 1 tablespoon oil and 1 tablespoon butter in a large nonstick skillet over medium-high heat. Add Brussels sprouts; sauté 2 minutes or until lightly browned. Add remaining 1/8 teaspoon salt and 1/4 cup broth to pan; cover and cook 4 minutes or until crisp-tender. Serve sprouts with chicken and sauce.