Heat olive oil in a large pot over medium heat. Add diced onions and sauté until translucent, about 5 minutes.

Add minced garlic and cook for another minute until fragrant, stirring constantly to prevent burning.

Add chopped tomatoes, vegetable broth, sugar, dried basil, and dried oregano. Stir well and bring to a boil.

Reduce heat to low, cover, and simmer for 20 minutes, stirring occasionally, until tomatoes are soft and flavors meld.

Use an immersion blender to puree the soup until smooth. Alternatively, transfer to a blender in batches and blend carefully.

Stir in heavy cream and season with salt and pepper to taste. Heat through for another 2-3 minutes.

Ladle into bowls, garnish with fresh basil leaves, and serve hot with crusty bread or grilled cheese.