Prepare the glass noodles according to the package directions. Drain, rinse thoroughly under cold water and drain again. Cut the noodles a few times with kitchen shears if you feel like making them easier to eat from the jars.
Pat the chicken dry and season with salt and pepper. Heat the neutral oil in a skillet over medium-high heat. Cook the chicken for 5 to 7 minutes per side, or until browned and cooked through. Rest for 5 minutes, then slice. You can use a rotisserie chicken too.
Whisk the peanut butter, soy sauce, lime juice, rice vinegar, honey, sesame oil, sriracha, garlic and ginger. Add warm water 1 tablespoon at a time until the sauce is pourable but still concentrated.
Divide the sauce among four large glass jars or mason jars. Layer in this order: cabbage, carrots, bell pepper, edamame, chicken, noodles, cucumber, scallions and cilantro.
Keep chilled. When ready to eat, invert the jar into a large bowl and toss thoroughly. Add a splash of water or lime juice if the sauce has thickened.
MAKE AHEAD Refrigerate up to 4 days. Let the noodles and chicken cool fully before assembling so steam doesn’t soften the vegetables.