Roast the Spaghetti Squash: Preheat the oven to 400°F. Cut the spaghetti squash in half lengthwise and scoop out the seeds. Lightly drizzle with olive oil and season with salt and pepper. Place cut-side down on a baking sheet and roast for 35–40 minutes, or until tender. Once cool enough to handle, use a fork to separate the flesh into spaghetti-like strands. Set aside.
Prepare the Sauce: In a small bowl, whisk together the fish sauce, rice vinegar, lime juice, peanut butter, honey, tamari, sriracha, and garlic until smooth. Adjust the sweetness or spice to taste.
Cook the Chicken: Heat the olive or avocado oil in a large skillet or wok over medium-high heat. Add the chicken, season lightly with salt and pepper, and cook for 5–7 minutes, or until cooked through. Transfer to a plate and set aside.
Scramble the Eggs: Add the sesame oil to the same skillet. Pour in the beaten eggs and scramble until just set.
Combine: Add the cooked spaghetti squash, shredded carrots, green onions, and chicken to the skillet. Pour the sauce over everything and toss until evenly coated and heated through. Fold in the bean sprouts, if using.
Garnish and Serve: Divide among four servings and top with crushed peanuts and fresh cilantro. Serve with lime wedges.