Heat the oven to 400 degrees. Snap the tough ends off the asparagus and discard them. Cut the asparagus spears into 1-inch pieces. Put the asparagus on a rimmed baking sheet and toss with the oil and ¼ teaspoon of the salt and ¼ of the pepper. Roast until tender, about 10 minutes. Remove from the oven and set aside. While the asparagus roasts, put the vinegar in a small saucepan. Simmer over medium heat until the vinegar is reduced to about 3 tablespoons, about 5-10 minutes. Stir in the brown sugar and the remaining ¼ teaspoon pepper. Remove from the heat. Cook the penne in a large pot of boiling salted water until just done, 11-13 minutes. Drain the pasta and return to the pot. Stir in the butter and vinegar mixture. Toss to combine well. Add in the asparagus, Parmesan, and the remaining ½ teaspoon salt. Serve immediately with additional Parmesan cheese for serving.