Add olive oil to a saucepan set over medium-low heat. Add onion and salt and cook, stirring frequently until onion has softened, about 5 minutes. Stir in tomato paste and continue to cook for 2 to 3 minutes, or until paste turns dark red in color.
Add pepper, tomatoes, water and brown sugar. Bring to a boil, then reduce heat. Simmer, uncovered for 20 minutes. Blend soup using a stick or jar blender until smooth.
Stir in heavy cream and season with more salt, to taste.
