Heat oil in a large soup pot or Dutch over over medium heat.
Add the onion, carrots, and celery. Cook, stirring occasionally, until the vegetables are softened and onions have lightly browned.
Stir in a the garlic and cook for an additional minute. Stir in the tomato paste and cook 20 to 30 seconds. Add the can of tomatoes, broth, salt, and pepper. Scrape up any brown bits stuck to the bottom of the pot.
Bring the pot up to a boil then cover and turn the heat down to simmer. Cook until the vegetables are very soft, 15 to 20 minutes.
Stir in the spinach and allow to wilt for a minute or two. Add the yogurt and brown sugar, if using.
Use an immersion blender in the pot to puree the soup until smooth. To use a regular blender, carefully transfer the soup and blend in batches then pour the soup back into the pot to reheat.
Taste the blended soup and stir in more salt and pepper as needed. Ladle soup into bowls then serve.
Notes
This soup is great served with the classic grilled cheese, any kind of bread, toast, or crackers. We like to make cheesy garlic bread with butter, garlic powder, and any kind of shredded cheese toasted on sliced bread.You can garnish soup with grated parmesan, a sprinkle of shredded cheese, fresh basil, or sliced fresh spinach leaves.