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.

I'll copy the translation here:

A hymn to Ninkasi (Ninkasi A)

1-4. Given birth by the flowing water ……, tenderly cared for by Ninḫursaĝa! Ninkasi, given birth by the flowing water ……, tenderly cared for by Ninḫursaĝa!

5-8. Having founded your town upon wax, she completed its great walls for you. Ninkasi, having founded your town upon wax, she completed its great walls for you.

9-12. Your father is Enki, Lord Nudimmud, and your mother is Ninti, the queen of the abzu. Ninkasi, your father is Enki, Lord Nudimmud, and your mother is Ninti, the queen of the abzu.

13-16. It is you who handle the …… and dough with a big shovel, mixing, in a pit, the beerbread with sweet aromatics. Ninkasi, it is you who handle the …… and dough with a big shovel, mixing, in a pit, the beerbread with sweet aromatics.

17-20. It is you who bake the beerbread in the big oven, and put in order the piles of hulled grain. Ninkasi, it is you who bake the beerbread in the big oven, and put in order the piles of hulled grain.

21-24. It is you who water the earth-covered malt; the noble dogs guard it even from the potentates (?). Ninkasi, it is you who water the earth-covered malt; the noble dogs guard it even from the potentates (?).

25-28. It is you who soak the malt in a jar; the waves rise, the waves fall. Ninkasi, it is you who soak the malt in a jar; the waves rise, the waves fall.

29-32. It is you who spread the cooked mash on large reed mats; coolness overcomes ……. Ninkasi, it is you who spread the cooked mash on large reed mats; coolness overcomes …….

33-36. It is you who hold with both hands the great sweetwort, brewing it with honey and wine. Ninkasi, it is you who hold with both hands the great sweetwort, brewing it with honey and wine.

37-40. 1 line fragmentary You …… the sweetwort to the vessel. Ninkasi, ……. You …… the sweetwort to the vessel.

41-44. You place the fermenting vat, which makes a pleasant sound, appropriately on top of a large collector vat. Ninkasi, you place the fermenting vat, which makes a pleasant sound, appropriately on top of a large collector vat.

45-48. It is you who pour out the filtered beer of the collector vat; it is like the onrush of the Tigris and the Euphrates. Ninkasi, it is you who pour out the filtered beer of the collector vat; it is like the onrush of the Tigris and the Euphrates.

The poem, as far as I can make out, is dated to ~1800 BC.

The beer would have been very different to what we would drink today, there would have been a lot of floaty things in there, and you would have drunk it with a straw to strain those out, as seen in this cylinder seal impression from the Ur III period.