8 chicken thighs with skin and bone 1 lb. button mushrooms, sliced 4 cups chicken stock or reduced-sodium chicken broth (32 fluid ounces) 2 stalks Bok Choy 2 TSP rice vinegar 2 TBSP garlic chile (also known as sriracha) 3 TBSP canola oil 2 large onions, coarsely chopped 1 lb fresh shiitake mushrooms, stems discarded, large caps quartered 3 TBSP finely chopped peeled ginger 3 TBSP finely chopped garlic 1 cup mirin 1 cup white miso 1/2 cup soy sauce 1 lb cabbage style greens, coarsely chopped
Preheat oven to 450°F with rack in middle.
Pat chicken dry, then roast, skin side up, in 1 layer in a 17- by 12-inch shallow baking pan until skin is golden brown, 35 to 40 minutes.
While chicken roasts, soak button mushrooms in 4 cups water until softened, about 15 minutes. Drain in a sieve, then rinse well and discard any hard pieces. Drain well, squeezing out excess water.
Transfer roasted chicken to a bowl and pour pan juices through a fine-mesh sieve into a 1-quart glass measure. Let stand until fat rises to top, 1 to 2 minutes, then skim off and discard fat. Add enough stock to bring total to 4 cups liquid.
Heat up the Crock Pot to High (300°F) or reduce heat in oven to that temp.
Clean and cut Bok Choy into one inch by one inch pieces. Soak in 2 cups water with vinegar.
Heat oil in a 7- to 8-quart heavy pot over medium-high heat until it shimmers, then sauté onions until softened and beginning to brown. Add shiitakes, ginger, and garlic and sauté until garlic is golden, 3 to 5 minutes.
Add mirin and boil, stirring and scraping up any brown bits, 1 minute. Stir in miso and soy sauce, then stir in chicken, button mushrooms, bok choy (drained), stock mixture, and garlic chile. Bring to a boil, skimming off any froth.
Pour into Crock Pot or cover pot and braise in oven until chicken is tender, about 1 hour.
Stir in cabbage style greens and continue to braise, covered, 5 minutes. Serve in shallow bowls with brown rice and garnished by chopped scallions.