In culinary uses, depending on the region of use (deviating in Scotland, where a 'cookie' is a type of bun, and in the UK, where what is called a 'cookie' in the US is called a 'biscuit'), a cookie is a usually a type of cake, distinguished from other types of cake by being small, flat, crisp, dry and sometimes sweet. As the core definition ('a little cake') suggests, in cookery the correct term for an oversized 'cookie' is cake. The type of cake is dry, sweet, flat, and crisp, but not small.
The culinary sense is supported by the etymology of cookie, where "Dutch koekje" is a "diminutive of koek cake" (from OED Online).
cook·ie also cook·y (ko͝ok′ē)
1. A small, usually flat and crisp cake made from sweetened dough.
[cookie. (n.d.) American Heritage® Dictionary of the English Language, Fifth Edition. (2011). Retrieved December 13 2015 from http://www.thefreedictionary.com/cookie .]
cookie (ˈkʊkɪ) or cooky
1. (Cookery) US and Canadian a small flat dry sweet or plain cake of many varieties, baked from a dough. Also called (in Britain and certain other countries): biscuit
2. (Cookery) a Scot word for bun
[cookie. (n.d.) Collins English Dictionary – Complete and Unabridged. (1991, 1994, 1998, 2000, 2003). Retrieved December 13 2015 from http://www.thefreedictionary.com/cookie .]
cook•ie or cook•y (ˈkʊk i)
1. a small, flat, sweetened cake, often round, made from stiff dough baked on a large, flat pan (cook′ie sheet`).
[cookie. (n.d.) Random House Kernerman Webster’s College Dictionary. (2010). Retrieved December 13 2015 from http://www.thefreedictionary.com/cookie .]
Chiefly Sc. and N. Amer.
1. In Scotland the usual name for a baker's plain bun; in U.S. usually a small flat sweet cake (a biscuit in U.K.), but locally a name for small cakes of various form with or without sweetening. Also S. Afr. and Canad.
["cookie, n.". OED Online. December 2015. Oxford University Press. http://www.oed.com/view/Entry/40961?redirectedFrom=cookie (accessed December 13, 2015).]