Bring a large pan of water to boil. Add whole tomatoes and simmer until skins split, scooping the tomatoes out of water with a slotted spoon as this occurs. Allow all tomatoes to cool. Cut off the stem ends and squeeze the tomatoes so that they slip out of the skins. Roughly chop the tomatoes while collecting the juice; strain and discard the seeds. Chop the tomatoes further into a fine dice, by hand or with a food processor. Add to the reserved juice.
Bring a large pot of water with 2 TBSP salt to a boil.
In a large frying pan, sauté onion in olive oil about 5 minutes on medium/low heat until translucent; add garlic and sauté a few more minutes. Do NOT brown. Remove to small bowl. Add the slices of pancetta and brown both sides slightly. This will not take long. Remove and set aside; continue until all pancetta slices are crisp and browned.
Melt 2 TBSP butter in the pan. Add chopped tomatoes and juice, salt and pepper. Put on the lid and cook on medium/low for about 10 to 14 minutes, stirring once in a while. Add fresh basil, turn sauce to low and return cover to top. Remove cover after 2 to 3 minutes, remove from heat, and swirl in last 2 TBSP butter into pan to thicken and emulsify the sauce.
Add the pasta to the boiling water, bring back to a low boil, and follow the cooking instructions on the box. Drain in colander, rinse, and drain well again, giving the colander a vigorous shake to remove any excess water, before tossing in the warm pasta pan with sauce, pancetta, and cheese. Toss and mix to distribute sauce evenly. Serve on warmed platter with more cheese, if desired.
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