Bring a large saucepan of water to a boil over medium-high heat. Turn off the heat. Add 8 ounces dried cornstarch noodles and make sure they are submerged. Let sit until softened, about 5 minutes. Drain.

Heat 1 tablespoon of the toasted sesame oil in a large wok or 12-inch frying pan on medium-high heat until shimmering. Add 1 pound boneless, skinless chicken breast chunks and spread into an even layer. Season with ½ teaspoon of the kosher salt. Cook undisturbed until browned on the bottom, 3 to 4 minutes. Stir-fry until lightly browned and cooked through, 3 to 5 minutes more. Transfer to a plate.

Add the remaining 1 tablespoon toasted sesame oil to the pan. Add 1 diced large yellow onion and 5 minced garlic cloves. Stir-fry until softened, about 2 minutes. Add 8 ounces peeled and matchstick cut carrots, season with the remaining 1 teaspoon kosher salt, and stir-fry until crisp-tender, about 2 minutes.

Add ¼ medium head shredded green cabbage and stir-fry until slightly wilted, about 2 minutes. Add 6 ounces snow peas and a few grinds of black pepper, and stir-fry until crisp-tender, about 2 minutes.

Add the noodles and chicken and any accumulated juices on the plate. Drizzle with ½ cup soy sauce and season with a few more grinds of black pepper. Stir-fry until combined, 1 to 2 minutes.

Add half of the sliced scallions (about 2 tablespoons) and stir-fry for 1 minute more. Taste and season with more kosher salt and black pepper as needed. Garnish with the remaining scallions and serve with lime wedges.