1. Combine 1 1/3 cups water and bulgur in a small saucepan; bring to a boil. Cover, reduce heat, and simmer 12 minutes; drain. Rinse with cold water; drain. Combine 1 tablespoon oil, 1 1/2 tablespoons vinegar, thyme, and ginger in a large bowl. Add bulgur, peaches, onions, 1/4 teaspoon salt, and 1/4 teaspoon pepper. Sprinkle with goat cheese.
2. Heat a large skillet over medium-high heat. Add remaining 1 tablespoon oil to pan; swirl. Sprinkle chicken with remaining 1/4 teaspoon salt and remaining 1/4 teaspoon pepper; cook 5 minutes on each side or until done. Remove chicken from pan; keep warm.
3. Add chicken stock to pan; cook 2 minutes, scraping pan to loosen browned bits. Stir in the remaining 1 tablespoon vinegar, peach preserves, and mustard; cook 1 minute. Spoon glaze over chicken. Serve chicken with bulgur mixture.