Cook the quinoa according to package directions, using broth instead of water. When done, stir in the 1/2 cup cheddar until melted inches.
Bring the 6 cups broth to a boil in a large pot. Peel and roughly chop the squash, garlic, and onion. Add to the pot of boiling broth. Cover and cook for 10-15 minutes or until squash is fork-tender. Optional: Set aside a cup of squash if you want to have pieces of squash in your soup for texture, if you want a totally smooth soup, add all of the squash.
Blend the soup with an immersion blender or in small batches in a blender. Add the curry paste, coconut milk, and salt. Puree again until incorporated.