Return the skillet to medium and add the garlic; cook, stirring, until light golden brown, about 2 minutes. Stir in the pepper flakes and cook until fragrant, about 30 seconds.
Add the wine, increase to medium-high and cook, stirring, until most of the liquid has evaporated, 5 to 7 minutes. Add the drained tomatoes and cook, stirring, until heated, about 2 minutes.
Meanwhile, in a large pot, bring 2 quarts of water and the pecorino chunk to a boil, stirring occasionally to prevent the cheese from sticking to the pot. Stir in the pasta and 2 teaspoons salt.
Cook, stirring often until the pasta is just shy of al dente. Remove and discard the pecorino, then drain the pasta in a colander set in a large heat-safe bowl; reserve the cooking water.
Set the skillet over medium-high, stir in 1½ cups of the reserved pasta water and bring to a simmer. Add the drained pasta, tossing with tongs. Cook, stirring occasionally until most of the liquid has been absorbed, 3 to 6 minutes.
Off heat, stir in the remaining 2 tablespoons oil, the pancetta and 2 teaspoons black pepper. Transfer to a serving bowl and serve with grated pecorino on the side.