Ash has been used one way or another in cooking for many hundreds of years. In South America, meat and fish are cooked in large pits of smouldering ashes over long periods of time, giving mouth wateringly smoky results. Native Indians would add ash to the water when cooking corn as it was believed to make the husks easier to remove, which in recent times it has been proven to have beneficial effects on health due to the calcium and potassium present in the ash.
In more recent times, ash has had a bit of a renaissance in modern cooking, being thrust into the limelight by Michelin-starred restaurants such as Noma in Copenhagen and Mugaritz in Spain. Noma features root vegetables such as celeriac which are rubbed with hay ash before being baked in a salt-crust pastry. At Mugaritz, they make ash from vegetables such as leek and horseradish.
The most commonly found use for ash is in cheese-making; this is an old process which was originally used to preserve the cheese as the alkaline ash neutralises the acidic surface of the cheese allowing for protective moulds to grow on the surface. The ash also soaks up moisture from the cheese preventing the mould from growing too rapidly.