Coat the bottom of a medium-sized saucepot with the oil and place it over medium-low heat.
Add the paprika, onions and garlic and cook until the onions are transluscent and soft, about 5 minutes.
Add the peppers and sauté for a minute or so. Then add the tomatoes, 2 large basil leaves, and balsamic. Cook for about 4 minutes, just to soften and blend the ingredients.
Add the water and bring to a boil. Then reduce the heat to low, cover the pot, and very gently simmer until the peppers are very tender, about 15 minutes.
Use an immersion or standing blender to purée the soup until it's as smooth as possible. (For this recipe, I prefer to use a blender -- it tends to create a smoother consistency.) Pour the soup back into the pot and add the salt, sugar and a few turns of freshly ground black pepper.
Drizzle each portion with a bit of extra virgin olive oil, if desired -- and top with a few small basil leaves.