Wash, trim and slice the asparagus spears into sections that match the size of the pasta. Beat the egg yolks. Grate the parmesan.
Put a pan of water on to boil. Heat one tablespoon of the butter in a wide bottomed pan and add the asparagus. Season it with a pinch of salt and stir it a couple of times. Cover if you like and let it cook gently while you pop the pasta into the boiling water. You can take the asparagus as far as you like, leaving it crunch or softening it up, but don't let it brown. When the pasta is done to your liking, drain it briefly and return it to the pot, off the heat.
Stir in the second tablespoon of butter and, immediately after that, the egg yolks, the seasoning and the asparagus. Stir quickly until you have a glossy emulsion around the pasta and asparagus. Don't be tempted to return the pan to the heat, as it will scramble the eggs.
Fold in the parmesan and test the seasoning. Service immediately.