Shiitake-Stuffed Chicken Breasts with Teriyaki Glaze

2 tsp dark sesame oil, divided
2 c sliced shiitake mushroom caps (about 1 [3.75-ounce] package)
2 tbsp minced green onions
1 tbsp grated peeled fresh ginger
3 tbsp low-sodium teriyaki sauce, divided
4 (4-oz) skinned, boned chicken breast halves
1/2tsp grated orange rind
1/4c fresh orange juice
1/4c dry wine
1 tsp honey
Sliced green onions (optional)

Heat 1 teaspoon oil in a large nonstick skillet over medium heat. Add mushrooms, minced green onions, and ginger, then sauté 3 minutes. Spoon into a small bowl, and stir in 1 tablespoon teriyaki sauce. Set aside. Cut a horizontal slit through the thickest portion of each chicken breast half to form a pocket. Stuff about 1 1/2 tablespoons of mushroom mixture into each pocket. Heat 1 teaspoon of oil in skillet over medium-high heat. Add chicken, and sauté on each side until chicken is done. Remove chicken from skillet. Set aside, and keep warm. Add 2 tablespoons teriyaki sauce, orange rind, orange juice, wine, and honey to skillet, and bring to a boil. Cook for 2 minutes or until reduced to a quarter of a cup. Spoon orange glaze over the chicken, and garnish with sliced green onions, if desired.