1 tablespoon plus 1/2 teaspoon salt
1 pound campanelli
3/4 cup balsamic vinegar
5 tablespoons extra-virgin olive oil
1 pound asparagus, tough ends snapped off, spears halved lengthwise if larger than 1/2 inch in diameter, and cut into 1-inch lengths
1 medium-large red onion, halved and sliced thin (about 1 1/2 cups)
1/2 teaspoon ground black pepper
1/4 teaspoon hot red pepper flakes
1 cup chopped fresh basil leaves
1 tablespoon juice from 1 lemon
2 ounces Pecorino Romano cheese, shaved (about 1 cup)
Bring 4 quarts of water to a rolling boil in a stockpot. Add 1 tablespoon salt and the pasta, stir to separate, and cook until al dente. Drain and return the pasta to the stockpot.
Immediately after putting the pasta in the boiling water, bring the balsamic vinegar to a boil in an 8-inch skillet over medium-high heat; reduce the heat to medium and simmer slowly until reduced to 1/4 cup, 15 to 20 minutes.
While the pasta is cooking and the balsamic vinegar is reducing, heat 2 tablespoons of the oil in a 12-inch nonstick skillet over high heat until it begins to smoke. Add the asparagus, onion, black pepper, pepper flakes, and remaining 1/2 teaspoon salt and stir to combine. Cook, without stirring, until the asparagus begins to brown, about 1 minute, then stir and continue to cook, stirring occasionally, until the asparagus is crisp-tender, about 4 minutes longer.
Add the asparagus mixture, basil, lemon juice, 1/2 cup of the Pecorino, and remaining 3 tablespoons oil to the pasta in the stockpot and toss to combine. Serve immediately, drizzling 1 to 2 teaspoons balsamic glaze over individual servings and passing the remaining Pecorino separately.