Preheat oven to 400°F. Brush squash halves with 1 tbsp oil, cut side down on a baking sheet; roast 35–40 minutes until strands pull easily.
Meanwhile, heat remaining oil in a skillet over medium-high. Cook chicken 5–7 minutes until browned and cooked through; remove and keep warm.
Whisk peanut butter, soy sauce, rice vinegar, honey, sesame oil, garlic, ginger, and red pepper flakes in a bowl. Add water to reach a pourable sauce.
Return chicken to skillet, pour sauce over, and simmer 2–3 minutes until glossy and coat well.
Use a fork to shred squash into strands. Divide squash onto plates, top with peanut chicken, green onions, and chopped peanuts.