Bring 4 quarts water to rapid boil in a large Dutch oven or pot over high heat.

Drain tomatoes reserving liquid. Puree half of tomatoes in a blender or food processor until smooth. Dice remaining tomatoes into 1/4-inch pieces. Combine both pureed and diced tomatoes in a measuring cup and add enough of reserved tomato liquid to equal 2 cups of tomatoes; set aside. Measure out vodka; set aside.

Heat oil in large heavy-bottomed saucepan over medium heat. Add onions, shallots, pepper flakes and tomato paste. Saute, stirring frequently, until onions and shallots just begin to turn light golden, about 3 minutes. Add garlic and stirring continuously, saute until fragrant, about 1 minute. Stir in tomatoes and 1/2 teaspoon salt. Remove pan from heat and add vodka*. Return pan to heat and bring to a brisk simmer over medium-high heat. Cook, stirring frequently, until strong alcohol flavor cooks off and sauce thickens, about 8 to 10 minutes. Stir in cream and cook until hot, about 2 minutes.

While sauce is cooking (right after adding vodka to sauce): Add 1 tablespoon salt to boiling water and drop pasta. Cook, stirring frequently, until molto al dente (about 1 minute shy of al dente - which is tender, but firm to the bite). Drain pasta well, reserving 1/4 cup cooking water. Return pasta back to Dutch oven, add sauce, and toss over medium heat until pasta absorbs some of the sauce, about 1 to 2 minutes. Add reserved cooking water, as needed, if sauce is too thick. Stir in basil and adjust seasoning with salt. Serve immediately, passing Parmigiano-Reggiano separately.

* Note: Drop the pasta into the boiling water just after adding the vodka to the sauce so that the sauce and pasta finish cooking at the same time.