Heat 1/2 teaspoon oil in a large nonstick skillet over medium heat. Add diced mushrooms and garlic; sauté 3 minutes. Stir in pepper, and set aside.
Cut a horizontal slit through the thickest portion of each breast half to form a pocket. Stuff 2 tablespoons mushroom mixture and 1 slice cheese into each pocket.
Heat 1/2 teaspoon oil in skillet over medium-high heat. Add chicken; cook 6 minutes on each side or until chicken is done. Remove chicken from skillet. Set aside; keep warm.
Add broth and Madeira to skillet. Bring to a boil; cook 2 minutes or until reduced to 3/4 cup. Combine cornstarch and water; add to skillet. Bring to a boil; cook 1 minute, stirring constantly. Return chicken to skillet; cover and simmer 2 minutes or until thoroughly heated. Serve sauce with chicken; garnish with mushrooms and thyme, if desired.