Place the tomato quarters and garlic on the lined sheet pan. Drizzle with 3 tablespoons of the olive oil and sprinkle the salt on top. Roast for 40 minutes.
While the tomatoes are cooking heat a Dutch oven over medium high heat. Add the remaining olive oil and onions. Stirring frequently cook until the onions caramelize. This can take up to 20 minutes.
Once the onions have caramelized reduce the heat to low. Once the tomatoes and garlic are ready add them, the oregano, paprika, chili flakes if you are using them, and the basil to the broth, increase the heat to medium, cover and cook for another 20 minutes.
If you are using an immersion blender, then carefully blend the soup to prevent splatter since it is still very hot. If not working in small batches add the soup and blend until smooth. Repeat until all of the soup has been blended.
Once the soup is ready to serve add the balsamic vinegar and mix well. Pour into bowls and drizzle 2 tablespoons of heavy cream on top. Top with additional basil. Pairs well with a grilled cheese sandwich or a nice crusty bread.