Penne with Roasted Asparagus and Balsamic Butter

1 pound asparagus
1 tablespoon olive oil
1 1/4 teaspoons salt
1/2 teaspoon fresh-ground black pepper
1/2 cup plus 2 tablespoons balsamic vinegar
1/2 teaspoon brown sugar
1 pound penne
1/4 pound butter, cut into pieces
1/3 cup grated Parmesan cheese, plus more for serving

Heat the oven to 400°. Snap the tough ends off the asparagus and discard them. Cut the spears into 1-inch pieces. Put the asparagus on a baking sheet and toss with the oil and 1/4 teaspoon each of the salt and pepper. Roast until tender, about 10 minutes.

Meanwhile, put the vinegar in a small saucepan. Simmer until 3 tablespoons remain. Stir in the brown sugar and the remaining 1/4 teaspoon pepper. Remove from the heat.

Cook the penne in a large pot of boiling, salted water until just done, about 13 minutes. Drain the pasta and toss with the butter, vinegar, asparagus, Parmesan, and the remaining 1 teaspoon salt. Serve with additional Parmesan.