Whole eggs are a great source of protein for your dog. Our holistic vet recommends egg be cooked with the whites cooked all the way through, as to not cause a biotin deficiency, but with the yolks still runny.
I buy local pasture raised eggs from a nearby ranch. This means the hens graze freely and eat natural grass as opposed to being kept confined and fed grains. Pasture raised hens are happy hens and their eggs have a higher level of omega-3 fatty acids.
When I serve eggs, I fry them in a little coconut oil and serve with some raw beef heart, kale, blueberries and carrot. My dog goes crazy for this meal and it's loaded with great nutrition. I also grind up some baked egg shell into a fine powder and add a pinch as a calcium source.