Preheat oven to 400°F. Halve squash, remove seeds, brush with oil, and roast cut-side down 35–40 minutes until tender.
Season chicken with salt, pepper, and a pinch of garam masala. Sear in a skillet with oil until browned and mostly cooked; remove.
Sauté onion until soft, add garlic and ginger, then spices; cook 1 minute until fragrant.
Add crushed tomatoes, simmer 8–10 minutes, then stir in yogurt or cream. Return chicken to sauce and simmer 5–7 minutes.
Scrape squash into strands, divide between plates, spoon tikka masala over, and garnish with cilantro.