Eggs are an excellent source of important nutrients for "Adrenal Fatigue" sufferers: methylcobalamin, choline, cysteine (via methionine?).
I'd heard that cooking eggs reduces nutrient content, but I don't remember which. Perhaps methionine/cysteine. I think the methionine/cysteine is concentrated in the yolks, so if you prefer to have your eggs cooked, you might soft boil them. [Wrong. Methionine is concentrated in the whites.]
I eat eggs from the six chickens we keep. Well, they're not producing a lot anymore, so we're supplementing from the store with organic, free range. I cook them all, though. Usually not a lot. I like my eggs runny.