Heat oven to 400°F. Cut squash in half lengthwise and scoop out seeds. Drizzle the cut sides with 1 tablespoon olive oil and season well with salt and pepper.
Lay on a parchment-lined baking sheet, cut side down. Bake in oven until knife tender and shreds easily with a fork, about 20-30 minutes.
Meanwhile, heat 3 tablespoons of the olive oil in a medium saucepan over medium-high heat. Add onions and season with salt and pepper. Cook, stirring occasionally, until tender, about 5 minutes. Add garlic and chipotles and cook a minute more. Add cream and broth and bring to a simmer. Cook until slightly thickened, about 5 minutes. Blend with a stick blender until smooth. Add teaspoon of salt, taste and add more salt if needed. Cover and keep warm.
Heat remaining tablespoon of oil in a small frying pan. Add breadcrumbs and season with salt and pepper. Cook, stirring constantly until toasted and golden. Transfer to a bowl and set aside.
To serve: Shred squash into strands, add to cream sauce and gently fold to coat in sauce. Divide between four plates, top with toasted breadcrumbs, sliced scallions, chopped cilantro, and Cotija cheese.