How to make it
Bring 3 quarts water to boil over high heat in stockpot. Meanwhile, combine chicken, 1 Tbsp soy sauce, and 1 Tbsp sherry in small bowl; set aside to marinate. Mix together hoisin, chili sauce, and remaining 1 1/2 Tbsp each soy sauce and sherry in small bowl; set aside while preparing noodles.
Add noodles and salt to boiling water; cook noodles until just tender(do not overcook), 2 to 3 minutes. Drain thoroughly, then toss with white and light green parts of scallions.
Heat 1 Tbsp. oil in 12" nonstick skillet over medium-high heat until shimmering, about 2 minutes. Spread noodles evenly across bottom of skillet; press with spatula to flatten and cook until crisp and golden brown, about 4 minutes. Slide noodle cake onto large plate. Add 1 Tbsp. oil to skillet, swirl to coat. Invert noodle cake onto second plate and slide it, browned-side up, back into skillet. Cook until golden brown on second side, about 4 minutes. Slide noodle cake onto cutting board; set aside.
Add 1 Tbsp oil to skillet; heat oil over medium-high heat until just beginning to smoke. Pour off excess liquid from chicken and add chicken to skillet; stir-fry until just cooked, about 2 minutes. Transfer chicken to small clean bowl.
Add remaining 1 Tbsp oil to skillet; heat oil over medium-high heat until just beginning to smoke. Add bok choy stalks and stir-fry 1 minute. Clear center of the pan, add ginger, and cook until fragrant, about 10 seconds, then stir ginger into stalks; continue to stir-fry until stalks are tender-crisp, about 20 seconds longer. Stir in bok choy greens, chicken, and hoisin mixture; cook until greens are wilted and ingredients are coated with sauce, about 30 seconds. Set skillet aside off heat.
Cut noodle cake into 8 wedges. Place 2 wedges on each of the 4 plates; spoon portion of stir-fry and sauce over noodle cake, sprinkle with scallion greens, and serve immediately.