Place the noodles in an extra-large bowl with warm water and let stand to soften, tossing occasionally, for 30 minutes.

Meanwhile, bring a large saucepan of water to a boil, add the bok choy pieces and simmer for about 1 minute until greens are wilted with crisp-tender stalks. Rinse with cold water until cool. In a small bowl combine 1 cup of the chicken broth with the soy sauce, honey, rice vinegar, and cornstarch; stir to blend and set aside.

When the noodles are ready, drain them in a colander in the sink.

In a large wok or deep, large skillet, heat 2 teaspoons of the oil over medium heat. Add the pork, breaking the meat apart with a spatula and cook, stirring once or twice, until barely pink. Move the pork away from the center of the pan, add another teaspoon of oil, the white scallion portions, garlic and ginger, then cook, stirring until fragrant and golden, 1 to 2 minutes. Stir the broth mixture to remix, then stir into the pork and scallion mixture. Cook, over medium heat until the sauce begins to thicken. Add the greens and mix to incorporate. Scrape the contents of the wok into a medium bowl.

Return the wok to the stove and increase the heat to medium-high. Carefully add the noodles, drizzle the remaining tablespoon of oil on top and cook, stirring and tossing for 2 minutes. Add the remaining 1/4 cup broth and continue cooking until the noodles are tender and nicely chewy, about 2 minutes more. Add the chicken-bok choy mixture to the noodles and toss until well mixed and heated through. Add the grapes, drizzle with sesame oil, and toss again.

Transfer with tongs to a serving platter or plates and sprinkle the scallions on top.