Meaning

noun a tall white hat with a pouched crown; worn by chefs

noun a small round woman's hat

origin1871. Assimilated from Canadian French tuque. Likely to be a hypercorrection from the time that toque was already in the dictionaries when they did not yet list tuque as a kind of hat. The French word tuque for hat is itself not strictly a deformation of French toque: it is also related to other meanings of tuque and to its former name bonnet à la turque (literally “Turkish-style bunnet/cap”).

Etymology from Wiktionary, CC BY-SA 3.0