I have not read all of the responses so forgive me if some of this was already covered.
There is no question that one of the healthiest foods on earth is the egg. For example, one egg has about 13 essential vitamins and minerals and 6 grams of high quality protein. Best of all an egg contains all 9 essential amino acids. And it has a whopping 600mg of leucine. And as you may know leucine stimulates muscle protein synthesis. That is exactly what you are after if you want to build muscle!
In addition to the above one egg has choline (for the brain) selenium (for the immune system), vitamin D which acts as a hormone in the body and helps us in more ways than I am able to list in a brief post. And also vitamin B12 for energy.
I am not denigrating whey protein at all and I think you should have your whey protein right after a workout as it will assimilate to your body (muscles) faster than any other type of protein. But don't forget to consume eggs at least three times a week. They will help you achieve your goal of building quality muscle and at the same time help keep you healthy in the long run!
Good Luck With Your Training,