Cook the onion in butter or olive oil until it begins to brown. Put all the vegetables in a pot and cover with 2 inches of water. The porportions of the vegetables may vary. Season with salt and pepper. Simmer for 10 minutes, then add the vermicelli and cook for 15 minutes more. Make the pistou while the soup cools. In a blender mix the garlic and basil. Gradually add the oil, then the Gruyere. Pour the soup in a tureen, mix in the pistou, and serve with a bowl of grated cheese.{$7e}(Original recipe for 6)