Boil, steam, or bake the asparagus until crisp-tender. Drain and transfer to paper towels. Pat the stalks dry and cut on the diagonal into 1-inch lengths.
Heat 3 tablespoons of the oil in a large skillet. Add the carrots and green onions and toss to coat. Stir over medium heat until the onions are limp. Add the remaining oil, lemon juice, parsley, and basil. Add penne and toss to coat with oil. Season with salt and pepper. Scatter the asparagus and pine nuts over the mixture and toss to combine. Stir over low heat until warmed through, then serve.