In a large saucepan, heat olive oil over medium heat. Add chopped onion and cook until translucent, about 5 minutes. Add minced garlic and cook for an additional minute.

Pour in the diced tomatoes with their juices. Stir to combine with the onion and garlic mixture.

Add vegetable broth to the saucepan. Bring the mixture to a boil, then reduce heat and let it simmer for 15 minutes to allow the flavors to meld.

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

Return the pureed soup to the saucepan over low heat. Stir in the heavy cream and shredded cheddar cheese until the cheese is melted and the soup is creamy. Season with salt and pepper to taste.

Ladle the soup into bowls, garnish with fresh basil leaves, and serve hot.