Preheat oven to 400 degree F and arrange rack in center; lightly oil a shallow baking pan. Place squash, cut side down, in pan and roast until tender, about 1 hour. Turn squash over and, when cool enough to handle, scoop out flesh into a bowl and mash.

While squash is roasting, pulse together cilantro, cheese, nuts, and chopped garlic in a food processor until finely chopped. Add 1/2 cup oil in a slow stream with the motor running until pureed. Transfer to a serving bowl; salt and pepper to taste, for pesto. (Can be made up to 2 days ahead. Keep chilled in an airtight container, covering surface with plastic wrap.)

Bring broth and 3 cups water to a simmer in a small saucepan. Remove from heat and keep warm, covered, Heat remaining 2 tablespoons oil in a large nonstick skillet over moderately high heat until hot but not smoking. Add onion and cook, stirring, until golden brown, about 8 minutes. Add sliced garlic and cook, stirring, 1 minute. Remove pan from heat. Stir in ginger and squash until combined well. Blend together squash mixture and broth (use caution when blending hot liquids), in batches, until smooth, transferring to a large saucepan.

Heat soup over moderate heat; season with salt and pepper. Add additional water if needed to reach desired consistency. Ladle soup into bowls and drizzle each with 1 tablespoon pesto. Serve remaining pesto on the side. Makes 8 servings.