Origin and history of roaster

late 13c., rosten, "to cook (meat, fish, etc.) by dry heat," from Old French rostir "to roast, burn" (Modern French rôtir), from Frankish *hraustjan (cognate with Old High German rosten, German rösten, Middle Dutch roosten "to roast"), originally "cook on a grate or gridiron," related to Germanic words meaning "gridiron, grate;" such as German Rost, Middle Dutch roost, from Proto-Germanic *raustijanan "to roast." Compare roster.

"Also freq. in mod. use to cook (meat) in an oven, for which the more original term is bake" [OED]. Intransitive sense of "be very hot, be exposed to great heat, become roasted" is from c. 1300. Of coffee beans by 1724. The meaning "make fun of (often in an affectionate way) for the amusement of the company" is from 1710. Related: Roasted; roasting.

Roast beef is recorded from 1630s; French rosbif is from English. 

Bifteck and rosbif, words that have come into French after the invasions of 1814 and 1815, are only imitations of the English way of pronouncing "beef-steak" and "roast beef," the French not recognizing their word rôti, formerly rosti, in the English sounds of "roast" nor bœuf, in that of "beef," which in Norman-French was written bœf and buef, and probably pronounced somewhat like the present English. [Jean Roemer, "Origins of the English People and of the English Language," London, 1888]