Combine boiling water and the sun-dried tomatoes in a bowl; let stand 15 minutes. Drain and chop.
Sprinkle chicken with 1/4 teaspoon salt and 1/8 teaspoon pepper. Heat the olive oil in a large nonstick skillet over medium-high heat. Add chicken, and sauté 5 minutes, turning once. Remove chicken from pan.
Reduce heat to medium-low. Add 1/4 teaspoon salt, 1/8 teaspoon pepper, and mushrooms; sauté 2 minutes. Add thyme, garlic, and bay leaf; sauté for 30 seconds. Return chicken to pan. Add sun-dried tomatoes, broth, and 1/4 cup wine. Cover, reduce heat, and simmer 25 minutes, turning chicken once.
Add 1 tablespoon wine and half-and-half, and bring to a boil. Discard bay leaf. Sprinkle with parsley. Serve over noodles.