Use a vegetable peeler to shave asparagus stalks into long, thin strips (about 2 1/2-3 cups shaved asparagus). Reserve the tips as well for the dish.
Fill a high-sided skillet with at least 2 inches water. Bring water to a boil over high.
Add pasta to skillet, and completely submerge; cook until al dente, about 8 to 12 minutes, use the directions on the package of pasta you are using.
Add shaved asparagus and tips to pasta; let everything simmer another 20 seconds or so.
Reserve 1/2 cup cooking liquid. Drain pasta and asparagus; return everything to the skillet. Reduce the heat to low or even off. If you are using cast iron, it will retain enough heat without the burner on.
Stir in reserved cooking liquid, 1 tbsp at a time, until sauce is slightly creamy and thoroughly coats pasta.
Toss with cheese and serve.
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