An archeologist has realized that food residues were included in the tomb of Midas in western Turkey from 2700 years ago. These residues were analyzed to produce a menu for the burial banquet for Midas. For appetizers Turkish meze of goat cheese, juliened cucumbers, asparagus, arugula, olive and garbanzo spread, dried figs, and cornelian cherry vinaigrette. The entree was a spicy lamb and lentil stew. The drink was a mixture of honey mead, beer, and wine with saffron added as a spice. The desert was a honey-carmelized fennel desert tart.  The book by Robert Garland contains a discussion of ancient Greek foods starting on page 91. Libations could be performed with either olive oil or wine. Sacrifices involved animals  which usually resulted in cooked meat. Harvest festivals would involve the harvested food, perhaps wine, olives, barley, or wheat.   Staples of the diet included cereals and vegetables, such as lentils, peas, beans, cabbages, asparagus, and garlic. Fish was plentiful but other meat was scarce. Honey was used but sugar was unknown. Flocks of goats and sheep furnished milk and cheese. Figs, and of course grapes, were the principal fruits but mention is made of apples, pears, pomegranates, and quinces. Citrus fruits, such as oranges and lemons, were unknown.
An example meal from ancient Greece could consist of a flatbread containing barley and a shishkabob with lamb, beans, cabbage, apples, and pears would work. Use olive oil and red wine to marinate the lamb. Thyme is a likely herb. Baklava for dessert.   Here is the oldest surviving recipe: "Take a wrasse. Wash it and cut into slices. Pour cheese and oil over it." Now cook it. (A wrasse is a fish).

In Book IX of the Illiad Achilles has a meal prepared for Aias (Ajax) and Odysseus. He instructs Patroclus "Bring out a bigger bowl,..., put less later in the wine, and give every man a cup." Later (Patroclus) "put down a big bench in the firelight, and laid on it the backs of a sheep and a fat goat and the chine of a great hog rich in lard. Automedon held these for him, while Achilles jointed them, and then carved up the joints and spitted the slices. Meanwhile, Patroclus, the royal son of Monoetius, made the fire blaze up. When it had burnt down again and the flames had dissapeared, he scattered the embers and laid the spits above them, resting them on dogs, after he had sprinkled the meat with holy salt.

When he had roasted it and heap it on platters, Patroclus fetched some bread and set it out on the table in handsome baskets; and Achilles divided the meat into portions.
In Book XXIV of the Illiad Achilles has a meal prepared for Priam. "The swift Achilles now bestirred himself and slaughtered a white sheep, which his men flayed and prepared in the usual manner. They deftly chopped it up, spitted the pieces, roasted them carefully and then withdrew them from the fire.
Automedon fetched some bread and set it out on the table in handsome baskets..." Then a handmaid bare water for the washing of hands in a goodly golden ewer, and poured it forth over a silver basin to wash withal, and drew to their side a polished table. And a grave dame bare wheaten bread and set it by them, and laid on the board many dainties, giving freely of such things as she had by her. And a carver lifted and placed by them platters of divers kinds of flesh, and nigh them he set golden bowls, and a henchman walked to and fro pouring out to them the wine.(Book I, Odyssey)

Even so they spake one to another, while the guests came to the palace of the divine king. They drave their sheep, and brought wine that maketh glad the heart of man: and their wives with fair tire sent them wheaten bread. Thus were these men preparing the feast in the halls. (Book IV, Odyssey)
And a handmaid bare water for the hands in a goodly golden ewer, and poured it forth over a silver basin to wash withal, and drew to his side a polished table. And a grave dame bare wheaten bread and set it by him and laid upon the board many dainties, giving freely of such things as she had by her. (Book VII, Odyssey)
Moreover a woman, a grinder at the mill, uttered a voice of women from within the house hard by, where stood the mills of the shepherd of the people. At these handmills twelve women in all plied their task, making meal of barley and of wheat, the marrow of men. (Book XX, Odyssey)
Men seemed to cook meat and women seemed to prepare bread, at least during the period of the Trojan war.