Preheat oven to 350°F. Line baking sheet with foil and coat with cooking spray. Place squash cut-side down on prepared baking sheet, and tuck garlic cloves in hollow under squash. Bake 50 minutes, or until tender. Cool 10 minutes. Scoop flesh from shell, and place in large bowl. Peel garlic cloves.
Heat large pot over medium heat, and coat with cooking spray. Add onion, and cook 7 minutes, or until translucent. Add ginger, allspice and cinnamon, and cook 1 minute more. Stir in squash, garlic, broth and 3 & 1/2 cups water. Bring to a simmer, and reduce heat to medium low. Partially cover pot, and simmer 25 minutes. Purée in blender or food processor until smooth. Serve hot or cold, and stir in chives and vinegar just before serving.
Using a large serrated knife, halve spaghetti squash lengthwise; discard seeds. Place both halves cut side down on a large piece of parchment paper, and microwave on high until just tender, 9 to 11 minutes. Use a fork to shred squash strands, and transfer to a large bowl.
In a small bowl, toss onion, lemon juice, and a pinch each salt and pepper.
In a nonstick skillet, heat 1 tablespoon olive oil and chopped garlic until beginning to turn golden brown. Add chickpeas; cook for 2 minutes. Toss with spaghetti squash, 1 tablespoon olive oil, and 1/4 teaspoon each salt and pepper. Fold in parsley and onion (and juices). Top with crumbled feta.