Cook noodles according to package; drain and set aside. Toss with a little oil to prevent sticking.
Whisk peanut butter, soy sauce, honey, rice vinegar, lime, sesame oil, garlic, sriracha, and warm water until smooth.
Heat oil in a large skillet over medium-high. Sear chicken 4–6 minutes until cooked through; remove.
Add peppers and carrots; sauté 2–3 minutes until crisp-tender. Stir in spinach until wilted.
Return chicken and toss with noodles and peanut sauce until everything is coated and warmed through.
Serve with chopped peanuts, cilantro, and lime wedges.