Bring a large pot of salted water to a boil over high heat.
Meanwhile, unroll the pancetta. Cut it into 1-inch long chunks, and then slice each chunk thinly across the grain.
Heat the olive oil in a large skillet over moderately low heat. Add the pancetta and cook until it renders some of its fat, about 5 minutes. Do not allow it to crisp. Add the onion and cook until soft, about 10 minutes. While the onion is cooking, add the pasta to the boiling water.
Add the red pepper flakes and parsley to the onion mixture and cook briefly to release their fragrance. Add the vinegar and simmer briefly until it evaporates, then add the tomato puree and 1/4 cup of the pasta water. Simmer briefly to blend.
When the pasta is just shy of al dente, drain it and return it to the warm pot over moderate heat. Add the sauce and cook briefly so the pasta absorbs some of the sauce, then transfer the pasta to a warmed serving bowl and shower with the pecorino. Serve immediately.
*Michael's Notes: Start boiling the pasta after the onions have softened so that you have some starchy pasta water for your sauce. Putting the pancetta in the freezer for about 30 minutes will make it easier to slice.