Bring a medium pot of water to a boil and salt the water generously. Prepare an ice bath for the tomatoes by filling a medium bowl with cold water and some ice cubes. Use a slotted spoon to plunge the tomatoes into the boiling water for about 1 to 2 minutes. The skin should show evidence of peeling away from the flesh of the tomatoes. Remove them from the water and plunge them into the ice bath. Allow the tomatoes to sit in the cool water so they stop cooking.
In a medium skillet, heat a tablespoon of the olive oil and add the garlic, shallots, and red pepper flakes. Season with salt and pepper. Add the oregano and sugar. Stir to blend. Allow to cook, over low heat, until the shallots and garlic become tender and translucent.
Meanwhile, remove the tomatoes from the ice bath, peel off and discard the skin from each. Place them on a flat surface, quarter them and scoop out the seeds and "jelly" from each piece. Gather all the seeds in a strainer and push through the liquid that naturally surrounds the seeds. Discard the seeds. Reserve the liquid and tomato flesh.
Add the tomato and liquid to the shallot mixture and stir in about 1 tablespoon of salt and 1 teaspoon ground pepper. Turn the heat down to medium and cook until the tomato flesh starts to lose shape, 8 to 10 minutes. Add the water and simmer for 15 to 20 minutes. If there are still some hard pieces, add a little more water and cook for a few more minutes. Taste for seasoning.
In a large pot, bring 6 quarts of water to a rolling boil. Add a generous amount of salt. The pasta water should taste like sea water. Add the pasta to the pot and stir so none of the pieces stick to the bottom as they cook. Cook the pasta until "al dente", chewy but not hard or raw tasting, 8 to 10 minutes, and drain the pasta in a colander until the sauce is finished. Reserve a little of the pasta cooking liquid in case you need it later.
Put the tomato sauce in the blender and puree until smooth. Slowly add the vinegar through the top of the blender as the sauce is blending. Next, pour the remaining olive oil through the top in a slow, steady stream. Blend in another cup of water then remove the sauce from the blender and taste for seasoning.
Pour most of the sauce into a large skillet and add the pasta. Toss to blend with a wooden spoon. If the sauce is too thick, add some of the pasta liquid to thin it out. Taste for seasoning. Add the basil leaves and sprinkle with cheese, if desired.