01 - Heat olive oil in a large pot over medium heat. Add diced onion and carrot. Sauté for 5 minutes until vegetables begin to soften and onion turns translucent.
02 - Stir in minced garlic and cook for 1 minute until fragrant, being careful not to brown or burn the garlic.
03 - Pour in diced tomatoes with their juices, fresh basil, vegetable broth, sugar, salt, black pepper, and red pepper flakes. Stir well to incorporate all ingredients.
04 - Bring mixture to a gentle simmer, then reduce heat to low. Cook uncovered for 20 minutes, stirring occasionally to prevent sticking and allow flavors to meld.
05 - Remove pot from heat. Using an immersion blender, puree the soup directly in the pot until completely smooth and velvety. Alternatively, transfer soup to a standard blender and blend in batches, taking caution with hot liquids.
06 - Pour in heavy cream and stir gently to combine. Return pot to low heat and warm through for 2-3 minutes. Taste and adjust salt and pepper as needed.
07 - Ladle hot soup into serving bowls. Garnish with additional fresh basil leaves. Serve immediately while hot.