Heat 1/2 teaspoon oil in a large nonstick skillet over medium heat.
Add 1/4 Cup of the onion, and cook until soft.
Add the garlic, and cook 1 minute.
Add spinach, and cook 3 minutes (until wilted).
Combine spinach mixture, cheese and mustard in a small bowl.
Wipe pan out with a paper towel. Cut a pocket in each chicken breast half and stuff spinach mixture into each.
Season chicken with salt and pepper.
Heat the other 1/2 teaspoon oil in skillet over medium-high heat.
Add chicken; cook 6 minutes on each side or until chicken is done (165 F). Remove chicken, tent with foil to keep warm and set aside while you make the pan sauce.
Add remaining 1 cup of diced onion to pan, and cook for about 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 thickened, add sour cream, stirring occasionally.
Return the chicken to skillet, cover and simmer 2 minutes or until thoroughly heated.
Serve sauce over the chicken.