Line a small plate with plastic wrap. Cut the cheese into 4 pieces. Moisten your hands lightly with cold water. Press and shape each piece of cheese into a heart shape. Set the hearts on the plate and refrigerate until needed.
Place oil in a pot over medium heat. Add onion and garlic and cook 3 minutes. Mix in flour and tomato paste and cook 1 minute. While stirring, slowly pour in the stock, and then add the diced tomatoes and sugar. Simmer the soup 10 minutes, and then stir in the basil. Purée the soup in a food processor, or in the pot with a hand blender, and then season with salt and pepper. Ladle the desired amount of soup into 2 bowls. (Any leftover soup can be cooled, refrigerated and enjoyed another time.) Carefully set 2 pieces of cheese into each bowl and serve.