- Heat oil in a pan. Add onion, carrot, and celery and cook for 5 minutes. onion, carrot, and celery in a pot Add broccoli,cauliflower, potato, bay leaf, and thyme. Add enough water to cover vegetables and salt. Bring soup to a boil, then cover and reduce heat. Simmer soup for about 20 minutes. Remove about half of the soup to a large measuring cup and blend. Return pureed soup to pot. Add remaining vegetables of your choice and the leafy greens. Cook until greens are tender. Season to taste with salt and pepper and serve.