Heat a large skillet over medium-high heat and add 1 tablespoon of the oil. When the oil just begins to smoke, add the sausage, breaking it into small pieces with a wooden spoon. Cook, stirring occasionally, until the sausage is browned and crispy, about 8 minutes. Transfer to a paper-towel-lined plate.
Reduce the heat to low. To the same skillet, add the red pepper flakes, garlic and shallots. Season with salt. Add the oregano and stir. Cook until the garlic and shallots are tender and translucent, 3 to 5 minutes.
Place a strainer over a medium bowl. Quarter the tomatoes and, working over the strainer, scrape the seeds and "jelly" from each piece. Push the liquid through the strainer and discard the seeds. Add the tomato flesh and liquid to the shallot mixture and stir in the sugar and 1 tablespoon salt. Reduce the heat to medium and cook until the tomato flesh starts to lose shape, about 10 minutes. Add 1/2 cup water and simmer until the tomato sauce is mushy, 15 to 20 minutes. Season with salt.
Meanwhile, bring a large pot of water to boil and add salt. Cook the pasta, stirring so it doesn't stick to the bottom, until al dente (chewy but not hard or raw tasting), 8 to 10 minutes. Drain the pasta, reserving a bit of the pasta cooking water, and set aside until the sauce is finished.
Transfer the tomato sauce to a blender and puree until smooth. Add the balsamic vinegar and blend again. With the blender running, pour the remaining 1/2 cup oil through the top in a slow, steady stream. Blend in 1 cup water then transfer the sauce to a large skillet and add salt to taste.
Place the skillet over medium heat and add the pasta. Stir to combine with a wooden spoon. Cook until the sauce and pasta are heated through, about 6 minutes. If the sauce is too thick, add some of the reserved pasta cooking water to thin it out. Drain any excess grease from the sausage and stir it into the pasta. Season with salt. Tear the basil leaves over the pasta and sprinkle with Parmesan.
When blending hot liquid, first let it cool for five minutes or so, then transfer it to a blender, filling only halfway. Put the lid on, leaving one corner open. Cover the lid with a kitchen towel to catch splatters, and pulse until smooth.