Feeding hard boiled chicken eggs
Welcome to BYC -- how old are the birds you are feeding? I don't have peafowl, but for chickens I do the folloiwng - for laying age birds, I prefer to crush the egg with shell on and feed it like that.....for juvenile birds I prefer to shell the egg prior to feeding.
People leave the shell on for calcium. Laying hens need a lot of it for their eggs. Since you said "he", they won't be needing the calcium so you are better off shelling it.