1. Preheat oven to 350°.
2. Heat a large Dutch oven over high heat; add oil to pan, swirling to coat. Add chicken; cook 4 minutes on each side or until browned. Add onion; stir-fry 4 minutes. Reduce heat; add broth and Shaoxing, scraping pan to loosen browned bits. Stir in ginger, oyster sauce, honey, and garlic. Cover and bake at 350° for 30 minutes.
3. Remove from oven. Shred chicken with 2 forks; return to pan. Place pan over medium-low heat. Add half of greens to pan; cover. Cook 5 minutes or until greens wilt; stir well. Repeat procedure with remaining greens. Cook mixture, covered, 15 minutes. Spoon 1 cup chicken mixture into each of 6 bowls; sprinkle each serving with 1/2 teaspoon sesame seeds.
The Shaoxing Redemption: Yes, you can use dry sherry in place of Shaoxing (shaow-SHEEN) wine, but we recommend adding this fragrant, deeply nutty wine to your pantry--you can experiment with it in stews or other recipes calling for winey flavor. Look for it in Asian markets, where a 750-ml bottle goes for between $4 and $10. But beware of bottles labeled "Shaoxing cooking wine"--the cooking variety has salt added.