Prep ingredients: Bring a large pot of salted water to boil. Pat chicken dry and pound to an even ½-inch thickness. Cut into ¼-inch thick strips. Trim ends from snap peas, then cut crosswise into 1-inch pieces. Trim ends from scallions, then thinly slice. Peel and finely chop 3 tablespoons ginger.

Cook pasta: Add pasta to boiling water and cook, stirring occasionally, until almost al dente, 8–9 minutes. Reserve ½ cup pasta water, then drain pasta well. Add all of the tamari, chicken broth concentrate, and 2 teaspoons each vinegar and sugar to reserved pasta water; whisk until sugar dissolves. Reserve for step 5.

Brown chicken: Season chicken with a pinch each salt and pepper. Heat 1 tablespoon oil in a large skillet over medium-high. Transfer chicken to skillet and cook until opaque, about 3 minutes. Add ginger and half of the scallions and cook until fragrant, about 30 seconds. Transfer to a plate.

Stir-fry vegetables: Heat 1 tablespoon oil in same skillet over high. Add snap peas, shredded cabbage, and a pinch each salt and pepper to skillet and cook until crisp-tender and browned in spots, about 3 minutes.

Build sauce: Add tamari-broth mixture to skillet with vegetables, stirring to combine.

Finish lo mein & serve: Transfer pasta, chicken and any juices, and 1¼ teaspoon of the sesame seeds to skillet with vegetables and sauce. Cook, stirring, until sauce coats pasta, about 1 minute. Remove from heat and season to taste with salt and pepper. Serve chicken lo mein garnished with remaining scallions and sesame seeds.