Place the pepper directly over a gas flame to char and cook, turning, about 3 minutes per side. Place the pepper in a bowl and let sit, uncovered, until cool enough to handle.
Place the pepper on a cutting board. Remove the seeds and core and open the pepper up so it lies flat on the cutting board, charred skin-side up. Use a kitchen towel to wipe the charred skin away. Sprinkle the pepper with the sugar, then chop the pepper into 1/4-inch dice. Place the diced peppers back in the bowl and drizzle with the vinegar. Set aside.
Bring 4 quarts water to a rolling boil in a large pot. Add a generous amount of salt. (It should taste like seawater.) Cook the pasta, stirring from time to time, until "al dente" (chewy but not hard or raw tasting), 8 to 10 minutes. Drain, reserving 1 cup of the pasta water.
Transfer the pasta to a large bowl and toss with the pesto. If the pesto is too thick, add some pasta water to thin it out. Place half of the pasta in a serving bowl, then top with half of the Parmesan and half of the roasted peppers. Top with the remaining pasta, Parmesan and roasted peppers. Garnish with fresh basil and serve.
Nut-Free Basil Pesto:
Yield: 1 cup
Pulse the basil with the garlic, sugar and salt in a food processor. Slowly stream in 1/2 cup olive oil and 1/4 cup water through the top of the machine, pulsing until almost completely smooth. Taste for seasoning. Add more oil if too chunky or dry. Transfer to a bowl and stir in the Parmesan.