The oldest cookbook I'm aware of the Apicius dated to the 4th century AD. You can read it at Project Gutenberg:

Apicius

Use Ctrl-F and search for Garum. There a couple of different Garum recipes. Interestingly enough, Worcestershire sauce is believed to be based on an old British version of Garum (if you look at the ingredients, you'll see that anchovies are a main component).

However, there are older references to certain foods usually embedded in larger works. These are usually not in great detail as the purpose of the author was rarely to teach another person how to cook something but rather to describe it in a general way. Even the Wikipedia page you link to quotes an ancient author about how garum was made. Certain old agricultural texts include descriptions for wine and beer. I was able to find an old issue of the The Oriental Institute newsletter on a beer recipe from 1800 BC:

Civil, M. (1991). "Modern Brewers Recreate Ancient Beer." The Oriental Institute News and Notes, no. 132, pp 1-4