As far as I can make out, the oldest written recipe is for beer. It is contained in a Sumerian hymn to the goddess of beer, Ninsaki.

You can read the translation of the hymn here, at the Electronic Text Corpus.

There have indeed been attempts to reconstruct various ancient cuisines. I personally have not read any of the cookbooks and so cannot offer much in the way of an opinion, but here are a couple of cookbooks that attempt to reconstruct some ancient cuisines:

Delights from the Garden of Eden: A Cookbook and a History of the Iraqi Cuisine. This book draws heavily on a number of ancient recipes, including some from cuneiform tablets and tenth century cookbooks.

Roman Cookery: Ancient Recipes for Modern Kitchens. This provides some recipes enjoyed from the Roman period as well as some explanations of the food and some of the cultural connotations of the meals.

Perhaps the best-researched one is the one I will leave for last.

A culinary journey through time : a cookery book with recipes from the stone age to the middle ages. This book used actual archaeological findings, rather than textual findings to reconstruct some ancient recipes. Data was derived from methods such as soil samples, paleoethnobotanical research, and other scientific laboratory-based methods.

As I said earlier, I am not an expert in gastronomic archaeology, and haven't read these books I am recommending, so if another expert has some critiques, I welcome them. But these are the ones I would start with, if I were to start playing around with ancient food ways.