Shell the beans, make them boil for just a few moments in boiling water, let them cool down immediately under cold water and, finally, peel them.
Cut the asparagus on the diagonal. Heat the oil in a quite big pan, brown the cloves of garlic in it, add the broad beans, cook for 2 minutes, then add the asparagus and the basil, then stir. Put salt and continue the cooking for some minutes more. At this point, cook the spaghetti al dente in salted water, strain them and pour them in the pan containing the prepared sauce. Then thicken it with cheese and serve it on very hot plates. Garnish with basil.