Add the tomatoes to a deep, large bowl. Using your hands, crush the tomatoes until no large pieces remain, just a coarse tomato puree.
Peel the garlic cloves and finely chop.
Heat the olive oil and butter in a large pot over medium heat. Add the onion and garlic and season with salt and pepper. Cook, stirring occasionally, until the onion is softened but not browned, about 10 minutes.
Add the anchovies and the oil they are packed in. Cook, stirring occasionally, until dissolved into the oil, about 2 minutes.
Add the red pepper flakes and stir to combine.
Add the tomato paste and cook until it turns a dark, brick-red color, about 4 minutes (this caramelizes the sugars in the tomato, which will give a really great flavor and take the edge off that raw tomato-y taste).
Add the wine and cook for about 1 minute, just to burn off the alcohol.
Add the tomatoes and stir everything together, making sure to scrape the bottom of the pot to get all those good bits. Add water and bring it to a boil.
Reduce the heat to medium-low and cook the sauce for 1½–2 hours at a very low simmer; there should just be a few bubbles here and there. If medium-low is too high (every stove is different), reduce the heat to low. Stir every 30 minutes.
Ladle out about 2 cups of sauce: This is what is known as your "extra sauce." You'll serve it alongside the pasta or freeze it for later.
To serve, cook the spaghetti in a large pot of salted boiling water.
Drain the pasta and add it to the sauce. Serve it right out of the pot, or transfer to a serving bowl. Top with grated Parmesan cheese.