Cook noodles according to package; drain and set aside.
Whisk peanut butter, soy sauce, lime juice, sugar, sesame oil, sriracha, and garlic until smooth; thin with 2–4 tbsp warm water if needed.
Heat oil in a large skillet over medium-high, cook chicken 5–6 minutes until browned and cooked through.
Add carrots and bell pepper, sauté 2–3 minutes until slightly tender.
Toss in noodles, spinach, and peanut sauce; heat until spinach wilts and everything is coated.
Serve topped with chopped peanuts and cilantro.