Heat the olive oil: Warm olive oil over medium-high heat in a large, deep pot.
Cook the veggies: Add the onions, carrots, celery, and minced garlic, stirring to coat. Let the mixture cook for about 8 minutes, allowing the vegetables to soften and release their flavors.
Add seasonings and tomatoes: Stir in the tomatoes, sugar, oregano, salt, and pepper. Pour in the vegetable stock and stir to combine everything.
Simmer: Bring the mixture to a boil, then reduce to a gentle simmer for 25 minutes, stirring occasionally.
Blend the soup: Carefully ladle portions of the soup into a blender (be sure to avoid overfilling). Blend in batches until smooth, and pour each blended portion back into the pot. If using a glass blender, allow the soup to cool slightly before blending.
Final seasoning adjustments: Mix the soup well once it’s all back in the pot, tasting and adjusting seasonings as needed.
Add heavy whipping cream: Stir in up to 1/4 cup of heavy whipping cream, starting with 2 tablespoons and adjusting to taste.
Serve: Ladle the soup into bowls, add your favorite toppings, and enjoy!