Trim the artichokes of their tough outer leaves and cut them into wedges. Place them in acidulated water.
Mince the garlic and parsley together until you have a very fine near-paste. Gently sauté the garlic and parsley in olive oil in a stainless steel, enameled or terracotta skillet, then add the artichoke wedges, which you will have drained but not too well. Toss the artichokes in the seasoned oil for a few minutes, seasoning generously with salt and pepper.
Add a glassful of water (or if you're in the mood, broth) to the skillet. Simmer uncovered over moderate heat until the liquid is nearly gone and the artichoke wedges perfectly tender. Add more liquid if it evaporates before the artichokes are done.
Whisk together egg yolks, lemon juice, grated cheese and tiny pinch of salt, along with a small pinch of minced parsley for color if you like.
Remove the skillet from the heat, then add the mixture to the skillet, mixing everything together so the artichokes are well covered. (Depending on how much residual heat is left in the pan, you may need to return the skillet to the burner over the gentlest heat possible.) Toss the artichoke wedges until the mixture has thickened into a creamy sauce. Take care not to scramble the egg.
Serve right away.