pastiche

Pastiche comes via French pastiche from Italian pasticcio, meaning "pie" or "something blended," which traces to Vulgar Latin *pastīcius, from Late Latin pasta ("dough, pastry cake, paste"), itself from Ancient Greek παστά (pastá, "barley porridge"), from παστός (pastós, "sprinkled with salt").

The word began as a description of blended, doughy food and was carried by Italian and French into the world of art and writing, where a "pastiche" became a work mixing together borrowed styles the way a pie mixes together ingredients.

Pastiche is a doublet of pasticcio, meaning both English words descend from the same Italian source but arrived by different paths.