"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.
<a href="https://www.etymonline.com/word/poached">Etymology of poached by etymonline</a>
Harper, D. (n.d.). Etymology of poached. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/poached