monster egg . how to
I would suggest finding a heat-resistant balloon of some sort, or a relatively spherical plastic bag, or even a round bag made from linen muslin. You steam the yolks in a small balloon, then cut it away once they're set.  Then you immerse this yolk in the whites, in a bigger balloon, and once again steam/boil this until set, and cut away the outer balloon.  This is based on one version of the Giant Egg recipe, where the egg parts were cooked in bottles which were then broken away.

If you want a shell, then your instinct for meringue, probably cooked with a blowtorch, might work, although it would be hard to avoid browning.  If you want something white, I'd suggest piping (and smoothing) royal icing in coils until you shell the whole egg.  This will dry quite hard and then can be cracked away for dramatic effect.

Note, though, that the monster egg won't be terribly good to eat.  The yolk will be way overcooked, as will the outer layers of the white, and pretty much certainly the yolk will have sunk to the bottom of the whites before they set.  And, ultimately, it's just a giant boiled egg. The purpose of this dish, like many other showpieces, is to be seen and not necessarily eaten.

Thanks for a fun and very original question, though!  And if you make it, send me a picture.