Heat 1/2 teaspoon oil in a large nonstick skillet over medium heat. Add 1/4 cup onion; sauté 6 minutes or until tender. Add garlic, and sauté 1 minute. Add spinach, and sauté 3 minutes. Combine spinach mixture, cheese and 1 teaspoon mustard in a small bowl. Stir well; set aside. Wipe pan dry with a paper towel.
Cut a horizontal slit through thickest portion of each chicken breast half to form a pocket. Stuff about 2 tablespoons spinach mixture into each pocket. Sprinkle chicken with pepper.
Heat 1/2 teaspoon oil in skillet over medium-high heat. Add chicken; sauté 6 minutes on each side or until chicken is done. Remove chicken from skillet. Set aside, and keep warm. Add 1 cup onion to pan, and sauté 5 minutes. Add wine and thyme; cook 3 minutes or until reduced by half. Add broth and 2 tablespoons mustard; cook 4 minutes or until slightly thick, stirring occasionally. Return chicken to skillet; cover and simmer 2 minutes or until thoroughly heated. Serve sauce with chicken.