Noun. Cooking, damn it. “…foods that seem to lend themselves most naturally to no-salt cookery are tomatoes, onions, mushrooms and eggplants.” (Craig Claiborne, New York Times, February 18 1981)/”…the volume is bolstered by essays on the role of African Americans in the evolution of American cookery …” (USA Today, February 15, 2011) Google Ngram.
notoneoffbritishisms.com 
I have to say as a Brit even I’d say cooking not cookery in the first example.
“Cookery” isn’t a straight synonym of “cooking”. In Britain, one would refer to a “cookery book” of recipes but never a “cooking book”.
Similarly, I don’t think any Brits would refer to “American cookery” either — it would be “cooking” or “cuisine”.
Is “cookery” just the old-fashioned word? I would agree with the above comments about its everyday usage. “Cookery book” is a phrase in its own right and perhaps therefore not subject to the change.
Cookery is a subject – e.g. of a book or college classes. Cooking is an activity or a skill. The meanings overlap but there is a difference.
“Cooking book”? Isn’t it “cookbook”?
We would say “cookery book”. You could say “cookbook” but it’s more prosaic. “cooking book” sounds like someones left it in the oven….