In a 4-5 quart pot over medium heat, saute the onion in butter until wilted, about 5 minutes.
Add the carrots, celery, cauliflower, potatoes, and water; increase heat to high, bring to a boil; reduce heat, and simmer gently, uncovered, stirring occasionally, until all the vegetables are very tender, about 25 minutes.
Stir in the peas and increase heat to high; when the soup begins to boil, the peas should be cooked.
Just before serving, season with salt and pepper to taste, stir in the parsley, lemon juice, and mint.
Variation-to make the soup thicker and more substantial, add 1/4 cup white rice with the vegetables.