Strain the tomatoes and reserve the juices.

Puree half of the tomatoes in a food processor until smooth.

Dice the remaining tomatoes into 1/2-inch pieces, discarding the cores.

Combine the pureed and diced tomatoes in a liquid measuring cup (you should have about 1 2/3 cups).

Add the reserved liquid to equal 2 cups.

Heat 1 tablespoon of oil in a large saucepan over medium heat until shimmering.

Add the pancetta (if using) and cook until crisp, 6 to 8 minutes.

Using a slotted spoon, transfer the pancetta to a small bowl and set aside.

Pour off all but 2 tablespoons of fat from the pan.

If not using pancetta, heat 1 tablespoon of oil in a large saucepan over medium heat until shimmering.

Add the onion and tomato paste and cook, stirring occasionally, until the onions are light golden around edges, about 3 minutes.

Add the garlic and pepper flakes; cook, stirring constantly, until fragrant, about 30 seconds.

Stir in the tomatoes and a pinch of salt.

Remove the pan from the heat and add the vodka.

Return the pan to medium-high heat and simmer briskly until the alcohol flavor is cooked off, 8 to 10 minutes; stir frequently and lower the heat to medium if the simmering becomes too vigorous.

Stir in the cream and cook until hot, about 1 minute.

Meanwhile, bring 4 quarts of water to a boil in a large Dutch oven over high heat.

Add 1 tablespoon of salt and the pasta.

Cook until just shy of al dente.

Drain the pasta, reserving 1/4 cup of cooking water, and transfer the pasta back to the Dutch oven.

Add the sauce to the pasta and toss over medium heat until the pasta absorbs some of sauce, 1 to 2 minutes, adding the reserved cooking water if the sauce is too thick.

Stir in the basil and the reserved pancetta and adjust the seasoning with salt.

Divide among pasta bowls and serve immediately, passing the Parmesan separately.