Preheat the oven to 400°F. Spread the diced butternut squash on a parchment-lined baking sheet and roast for 10–14 minutes, until tender. Set aside.
In a large skillet over medium heat, add the roasted squash, diced onion, grated ginger, and chicken broth. Simmer for 2–3 minutes, until the onion softens.
Stir in the cooked chicken. Sprinkle the cinnamon evenly over the mixture and toss to coat.
Season with salt and black pepper to taste.
Bring a pot of water to a boil. Add the pasta and cook for 3–4 minutes. Drain well.
Combine:
Add the cooked pasta and arugula to the skillet. Toss gently until the arugula wilts and everything is evenly combined. Adjust seasoning if needed.
Serve:
Divide into bowls and top with toasted walnuts.