Step 1

Combine chicken, 1 cup broth and 1 tablespoon ginger in a small saucepan; bring to a simmer over medium-high heat. Cover, reduce heat to maintain a simmer, and cook, turning once or twice, until an instant-read thermometer inserted into the thickest part of the chicken registers 165 degrees F, about 15 minutes. Transfer the chicken to a clean cutting board (reserve the poaching liquid). When cool enough to handle, shred the chicken and set aside.

Step 2

Add peanut butter, soy sauce, vinegar, chile oil, sugar and the remaining 1/4 cup broth to the reserved poaching liquid; whisk until well combined. Set aside.

Step 3

Bring a large pot of water to a boil. Cook noodles according to package directions. Drain and rinse well.

Step 4

Heat a 14-inch flat-bottom carbon-steel wok or large cast-iron skillet over medium-high heat. Add 1 1/2 tablespoons peanut (or canola) oil and swirl to coat. When the first puff of smoke appears, add the remaining 2 tablespoons ginger, garlic and crushed red pepper; cook, stirring, until very fragrant but not browned, 10 to 20 seconds. Stir the garlic mixture into the peanut sauce in the saucepan; bring to a simmer over medium heat, then remove from heat.

Step 5

Place the wok over high heat. Add the remaining 1 1/2 tablespoons peanut (or canola) oil and swirl to coat. When the first puff of smoke appears, add bok choy and cook, stirring, until crisp-tender, 1 to 2 minutes. Remove from heat.

Step 6

Add the noodles to the bok choy and gently toss to combine. Transfer to a large shallow serving bowl. Top the noodles with the chicken. Reheat the peanut sauce, if desired, and pour over the noodles. Drizzle sesame oil over the top and sprinkle with scallions and sesame seeds. Toss together at the table before serving.