"cook in boiling liquid," mid-15c. (implied in pocched egges), from Old French poché, past participle of pochier (12c.), apparently literally "put into a pocket" (perhaps as the white of an egg forms a pocket for the yolk), from poche "bag, pocket," from Frankish *pokka "bag," from Proto-Germanic *puk- (see poke (n.1)). But connection to poke (v.) via the notion of a "broken" (shell-less) egg also has been proposed.
Pochee as a noun in reference to a way of preparing eggs is attested in a late 14c. cookery book, and eyron en poche for "poached eggs" is attested from early 15c. Related: Poaching.
monstrous predatory bird of Arabian mythology, 1570s, from Arabic rukhkh, from Persian rukh. It is mentioned in Marco Polo's account of Madagascar; according to OED, modern use of the word mostly is due to translations of the "Arabian Nights" tales. Hence roc's egg "something marvelous or prodigious." Compare simurgh.