Preheat the oven to 400 degrees. Place the asparagus on a sheet pan and drizzle with 1 tablespoon olive oil and season with 1 teaspoon salt and ½ teaspoon pepper. Toss to coat and roast for 10 minutes. Cut into 1- to 2-inch pieces.
Meanwhile, bring a large pot of heavily salted water to a boil. Add the penne and cook according to the package directions. Drain, reserving about 1 cup of the pasta cooking water.
In a large skillet, melt the butter over medium heat. Add the shallot and cook, stirring occasionally, until softened and beginning to brown, about 5 minutes. Add the garlic and cook for 30 seconds, stirring. Add the pasta, asparagus, and Parmesan cheese plus ½ cup of the reserved pasta cooking water. Stir until the cheese has melted. If the pasta seems too dry, add a little more of the pasta cooking water. Stir in the chives. Taste and add salt and pepper, to taste.
Serve with more Parmesan cheese and a drizzle of olive oil, if desired.