I'm not so sure the beer in the OP is the oldest as I found a recipe a couple of years older.
An Ancient Recipe for Beer
If you look at a field of wheat and a loaf of bread, you wouldn't guess that one came from the other. But we've known about the relationship for at least 10,000 years.
Bread really is the Staff of Life
Beer is liquid bread, and in ancient Sumer, beer making and bread making were different sides of the same coin. The Sumerians left us a recipe, on a clay tablet, for making beer.
It's the oldest recipe in the world.
Beer was made thousands of years ago in ancient Mesopotamia, and actual brewing records exist from this "dawn of civilisation."
These records are written in cuneiform script on clay tablets.
Hymn to Ninkasi
Ninkasi is the ancient Sumerian Goddess of brewing and beer and head brewer to the gods themselves. Her name means "The Lady who fills the mouth".
The Electronic Text Corpus of Sumerian Literature (ETCSL), a project of the University of Oxford, comprises a selection of nearly 400 literary compositions from ancient Mesopotamia.
One text, the Hymn to Ninkasi, is a set of instructions for making beer. It tells of baked grains being broken into pieces and stuffed into a pot. Water and aromatics are added (creating a basic mash and wort) and left to ferment.
You can read the Hymn to Ninkasi from ETCSL or stick with the easier-to-read text below.
The Ancient Recipe for Beer
You are the one who handles the dough with a big shovel,
Mixing in a pit, the bappir with sweet aromatics,
Ninkasi, you are the one who handles the dough with a big shovel,
Mixing in a pit, the bappir with honey,
You are the one who bakes the bappir in the big oven,
Puts in order the piles of hulled grains,
Ninkasi, you are the one who waters the malt set on the ground,
The noble dogs keep away even the potentates,
You are the one who soaks the malt in a jar,
The waves rise, the waves fall.
You are the one who spreads the cooked mash on large reed mats,
You are the one who holds with both hands the great sweet wort,
The filtering vat, which makes a pleasant sound,
You place appropriately on a large collector vat.
Ninkasi, you are the one who pours out the filtered beer of the collector vat,
Like the onrush of Tigris and Euphrates.
Don't forget the bread, a byproduct of making beer
Bappir is a twice-baked barley bread.
Here's a modern recipe for Bappir Bread
Hulled grains have the outermost hull removed (not the bran)
The ancient Sumerians kept their beer in large jars and drank them in a communal fashion.
These beers were often thick, more of a gruel than a beverage, so straws were used. Two or more drinkers would sip the beer through a straw, possibly to filter out impurities (through the teeth) or to avoid sludge at the bottom of the jar.
Perhaps they just liked drinking together.
Beer was so important that in the Code of Hammurabi (18th century B.C.E), beer shop owners who overcharged customers were to be put to death by drowning. (hopefully not in the beer vats).