Bring a large pot of lightly salted water to a boil. Add penne and cook, stirring occasionally, until tender yet firm to the bite, about 11 minutes. Drain.
While the pasta is cooking, heat 3 tablespoons oil in a large skillet over medium-high heat. Stir in chicken and season with ¼ teaspoon garlic powder, salt, and pepper. Cook and stir until chicken is browned and the juices run clear, about 5 minutes. Transfer chicken to a paper towel-lined plate.
Pour chicken broth into the skillet. Add asparagus, garlic, and another pinch of garlic powder. Season with salt and pepper. Cover and steam until asparagus is just tender, 5 to 10 minutes. Return chicken to the skillet and cook until heated through, 2 to 3 minutes.
Transfer drained penne to a large bowl. Pour chicken mixture over top and mix until well combined. Let sit for about 5 minutes.
Stir in remaining 2 tablespoons olive oil, then sprinkle with Parmesan cheese.