Preheat oven to 400°F. Drizzle squash halves with 1 tbsp olive oil, season, and roast cut-side down 30–35 minutes until tender.
Scrape squash into strands and set aside.
Heat remaining oil in a large skillet over medium-high heat. Add chicken, season, and cook 6–8 minutes until browned and cooked through.
Whisk mustard, honey, vinegar, garlic powder, and paprika in a small bowl. Pour over chicken, stir to coat and simmer 2 minutes.
Add spaghetti squash strands and spinach to skillet, toss until heated and spinach wilts. Adjust salt and pepper, garnish with parsley, and serve.