Bring a large pot of water to a boil; add 1 tablespoon salt; then drop in the asparagus; boil 3-5 minutes, until just tender; remove from water using a slotted spoon; refresh with cold water and set asparagus aside.
Chop the garlic in food processor fitted with a steel blade; when it adheres to the sides, stop the machine and scrape down the sides.
Add the cottage cheese; blend until fairly smooth; scrape down the sides.
Add in the milk; blend again until smooth; add salt and pepper to taste; transfer to a wide pasta bowl.
Bring the water in the pot back to a boil; add in the pasta; stir to make sure the pasta doesn’t stick to the bottom of the pot; cook until al dente; reserve ¼ cup cooking water and drain pasta.
Stir the reserved cooking water into the cottage cheese mixture; add the pasta, asparagus, chives, and pecorino; toss to combine; serve hot.