1. In a nonstick skillet, heat 1 teaspoon of oil.
2. In a medium bowl, mix 2 tablespoons of vinegar, the mustard and garlic. Add chicken and turn to coat.
3. Transfer chicken and marinade to skillet. Saute chicken until cooked 80% through, about 2 minutes on each side.
4. Top each piece of chicken with 1 teaspoon goat cheese. Transfer chicken to broiler or 350 degree oven and cook another 2-3 minutes.
5. Heat remaining teaspoon of oil in skillet. Saute mushrooms for 1 minute. Add broth, thyme and remaining tablespoon of vinegar. Cook, stirring occasionally, until mushrooms are deep brown, about 2 minutes longer.
6. Serve chicken topped with mushrooms.
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