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 edges become translucent.
02 - Stir in minced garlic and cook for 1 minute until fragrant, being careful not to brown the garlic.
03 - Add diced tomatoes with their juices, chopped basil, vegetable broth, sugar, salt, black pepper, and red pepper flakes. Stir thoroughly to combine 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. Use an immersion blender to puree the soup until completely smooth and creamy. Alternatively, carefully blend in batches using a standard blender, venting lid to release steam.
06 - Pour heavy cream into the pureed soup and stir to incorporate. Reheat gently over low heat for 2 to 3 minutes until warmed through. Taste and adjust salt and pepper as needed.
07 - Ladle hot soup into individual bowls. Garnish each portion with fresh basil leaves and serve immediately while hot.