Put thelemon halves face down on a cutting board and slide your knife between them soit's pointing toward the pith (the white stuff). Cut enough to get at theyellow part of the lemon but be careful to not cut all the way through.
Place eachfilet in its own pan with a glass lid and place the lemon halves on top ofthem.
Add wateruntil it just reaches beneath the fish. Pour out any excess that you don't need.
Heat upenough butter to coat four filets, about 1 tablespoon per filet, and add thelemon juice until it's equal in volume to the butter.
Remove fromheat and mix in egg yolks, then add salt and pepper to taste.
Poach thefish for about 10 minutes or until cooked all the way through. Serve withsauce. I also like to serve with some vegetables such as two asparagus or apiece of carrot
Notes
You can also serve your poached salmon with another type of sauce according to your preferences.