Bring 4 litre of salted water to a boil in a large pot for cooking the pasta.
Snap off the tough ends from the asparagus spears. Cut the spears in half lengthwise (thicker spears should be quartered), then slice them on the bias into 3 cm pieces. Steam the asparagus until crisptender, about 2 minutes. Set the cooked asparagus aside.
Combine the two cheeses with the basil, salt, and pepper in a medium bowl. Set the mxiture aside.
While preparing the sauce, cook the pasta. Just before it is done, carefully remove one third cup of the cooking liquid and stir it into the cheese mixture. The cheese sauce should be smooth and creamy.
Drain the pasta, making sure that some water still clings to the noodles. Toss the hot pasta with the ricotta mixture and asparagus. Mix well to coat the pasta with the sauce. Transfer portions to warm pasta bowls and serve immediately.