E. Cobham Brewer 18101897. Dictionary of Phrase and Fable. 1898.
Brew me a glass of grog, i.e. mix one for me. Brew me a cup of tea, i.e. make one for me. The tea is set to brew, i.e. to draw. The general meaning of the word is to boil or mix; the restricted meaning is to make malt liquor.