Season the chicken with salt and pepper. In a small bowl, blend the cornstarch into the water or broth.
Heat 2 tsp. of the oil in a medium sauté pan over medium-high heat. Add the snow peas and cook, stirring frequently, until they're slightly browned and softened but still crisp, 2 to 3 min. Transfer to a medium bowl. Heat another 1 Tbs. oil in the pan and add the chicken. When the underside of the chicken has turned deep golden brown (after about 1 min.), turn it with a metal spatula. Turn occasionally for even browning until almost cooked through, 3 to 5 min. Add the chicken to the bowl of peas.
Heat the remaining 1 tsp. oil in the pan. Add the ginger and cook until fragrant, about 1 minute. Reduce the heat to medium, add the garlic, and cook until fragrant, about 30 seconds. Add the sake or mirin, soy sauce, vinegar, honey, and the cornstarch mixture. Use a wooden spoon to scrape up any browned bits in the pan and blend them into the sauce. Bring to a boil, reduce the heat to medium low, and toss the chicken and snow peas into the sauce. Season with salt and pepper to taste. Serve immediately, sprinkled with the sprouts or cilantro.