Marinate diced chicken with soy sauce, olive oil, and honey for at least 15 minutes.
Bring a large pot of salted water to a boil and cook noodles until al dente according to package instructions. Reserve ½ cup pasta water and drain.
Heat a large skillet over medium heat with a drizzle of sesame oil. Add the chicken, discarding the marinade, and cook 4 minutes per side until browned and cooked through. Transfer to a bowl tented with foil.
In the same skillet, add another drizzle of sesame oil and cook diced shallots for 3–4 minutes until softened.
Add minced garlic and cook 30 seconds, stirring constantly until fragrant.
Reduce heat to medium-low. Add in peanut butter, gochujang, chili oil, sesame seeds, soy sauce, and lime juice. Cook for 1–2 minutes until the peanut butter melts and forms a thick paste.
Pour in the coconut milk and whisk until smooth. Bring to a gentle simmer and cook for 2–3 minutes.
Add cooked noodles and toss until evenly coated in the sauce. Add reserved pasta water if needed to loosen the sauce.
Top with cooked chicken and garnish with cilantro, green onions, and extra chili oil.