To peel the tomatoes.

1. Heat a kettle or pot of water to a boil.
2. While the water is heating up, cut an X on the bottom of each tomato to make it easier to peel.
3. Place the tomatoes into a big heat-proof bowl.
4. When the water has begun to boil, pour the hot water over the tomatoes and let sit for 2 minutes.
5. Drain the water and remove the tomatoes (But keep the bowl handy). Let cool briefly, as they are hot.
6. The skins should easily peel right off.
7. Quarter the tomatoes and remove the core.
8. Place the tomatoes back in the bowl and set them aside.
9. Heat 2 Tbsp of the olive oil in a wide-bottomed Dutch oven or saucepan. Over a very gentle heat, sauté the onions until they are soft but not browned.
10. Add the garlic and let cook for one minute to get fragrant.
11. Turn up the heat to medium and add the tomatoes to the pan.
12. Let the mixture boil, then turn the heat back down and let simmer covered for one hour, stirring occasionally.
13. You can use a potato masher to encourage the tomatoes to break up further if you wish, or I used a stick blender to get it really smooth.
14. Optionally if you want to get all fancy, I passed the puree through a fine mesh strainer to get all the seeds out and placed the puree back in the pot. It is fabulous either way.
15. Add the remaining 2 tablespoons of olive oil, balsamic vinegar, and sugar to the pan. Bring it back to a gentle simmer and cook for an additional 30 minutes or so to thicken, stirring occasionally.
16. Take off the heat and stir in the ¼ cup of parmesan cheese.
17. Taste the sauce to see if it needs any more salt.
18. When ready to use, add the fresh basil and more parmesan cheese if desired