In my opinion an egg sandwich isn't an option.
It's as good as impossible to carry chicken eggs in the rucksack.
And it is very complicated to domesticate squirrels to bring us the eggs of other birds down from the trees.
Even a domesticated rat, how you can easily buy it every where, would eat the eggs in the tree alone and wouldn't share it with you.
And if it would bring you some eggs, you would have the problem, that usually your bread would be to large for the egg the squirrel or rat brought you. So that doesn't look nice!
Bread in such little sizes you will not find at the market!
As you see:
The whole Idea is every thing else than practical!
;0(