Add chopped bell peppers, green onion, garlic, basil, and red hot sauce. Stir occasionally for 5-10 minutes, or until peppers become soft.
Stir in tomato juice, water, and salt.
If you have a hand-held blender, you can blend the soup right in the pot. If not, remove a few cups at a time (or enough to fill your blender halfway) and blend to a smoothie-like mixture. Pour the blended soup into a bowl and repeat with the rest of the soup, a few cups at a time, until all of it has been blended. Pour the soup from the bowl back into the pot. Note: If you prefer a smoother soup, blend longer - but I don't suggest any chunkier, as the skins of the peppers will be too noticeable.
Add the milk and yogurt, and stir to blend.
Let simmer on low heat for 5-10 minutes. Serve with parmesan sprinkled over top.