Add 1 teaspoon of the olive oil to a skillet. Saute asparagus over medium-high heat until lightly browned and tender-crisp. Remove from pan and allow to cool. Cut into 1-inch pieces.
Fill a large pot 3/4 full with water and bring to a boil. Add the pasta and cook until tender (al dente), 10 to 12 minutes, or according to the package directions. Drain the pasta thoroughly.
Put the pasta into a large bowl. Drizzle the remaining 1 teaspoon olive oil over the pasta and toss gently. Add the tomato, garlic, basil, asparagus, and 2 tablespoons of the Parmesan. Toss to mix evenly.
Divide the pasta between individual plates. Top each serving with 1 tablespoon Parmesan and black pepper, as desired. Serve immediately.