"peculiarity" (physical or mental), 1680s, from Latinized form of Greek idiokrasia, from idios "one's own, personal" (see idio-) + krasis "mixing, tempering," from PIE root *kere- "to mix, confuse; cook" (see rare (adj.2)). Related: Idiocratic.
[undercooked] 1650s, a variant of Middle English rere, from Old English hrere "lightly cooked," probably related to hreran "to stir, move, shake, agitate," from Proto-Germanic *hrorjan (source also of Old Frisian hrera "to stir, move," Old Saxon hrorian, Dutch roeren, German rühren, Old Norse hroera), from PIE root *kere- "to mix, confuse; cook" (source also of Greek kera- "to mix," krasis "mixture").
Originally of eggs, not recorded in reference to meat until 1784, and according to OED, in this sense "formerly often regarded as an Americanism, although it was current in many English dialects ... and used by English writers in the first half of the 19th c."
<a href="https://www.etymonline.com/word/idiocrasy">Etymology of idiocrasy by etymonline</a>
Harper, D. (n.d.). Etymology of idiocrasy. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/idiocrasy