To a medium pot, heat olive oil over medium-high heat. Once hot, add onion and carrots and cook for 5-6 minutes until fragrant and lightly golden.
Then, add garlic, tomato paste, and chili flakes (optional) and cook for a further 2-3 minutes or until the tomato paste is caramelized and darkened in color. Add a little bit of oil or water if the bottom starts to burn.
Crush the tomatoes with your hands and add them to the pot, alongside the vegetable broth, sugar, fresh basil, salt and black pepper. Stir and bring to a boil. Turn the heat to medium and cook for 20-25 minutes or until the carrots are soft and the soup has thickened.
At this point, you can add the feta and blend it with the soup, but I prefer to add it just before serving for texture. Using an immersion blender, blend until creamy and smooth. (If are using a standard blender it's important to let the soup cool a bit before transferring it. Don't fill the jar more than halfway and make sure that you leave the hole in the lid open so that heat can escape).
Lastly, stir in the cream (optional), and serve into bowls. Top with the crumbled feta (if you haven't added it already in the previous step), a drizzle of olive oil, and serve with grilled cheese on the side!