Bring a large pot with lightly salted water to a boil. Cook udon in boiling water, stirring occasionally, until noodles are tender yet firm to the bite, 10 to 12 minutes. Drain; return to the pot.
Meanwhile, whisk chicken broth, soy sauce, peanut butter, garlic, chili oil, ginger, and honey together in a saucepan over medium-high heat; bring to a boil, whisking until peanut butter melted.
Pour sauce over noodles; stir in chicken and bell pepper and toss until noodles are evenly coated in sauce. Sprinkle with green onions, chopped peanuts, and cilantro; serve.