Whats this cooking method called where you bury the food (potato, sugarbeet, guava, corn cobs)in hot charcoal ashes?
This is just traditional fire cooking, now called camp-fire cooking, or (US) cowboy cooking
Any Scout should know how to do this :-)
It works best using food with tough outer skins, or wrapped in a sacrificial coverings, or more modernly using aluminium foil, or a cast iron pot (dutch oven)
Some common foods examples:
Potato and other Tubers
You lose about 5 mm (including unpeeled skin) to the fire. If you wrap in Aluminium foil the loss is often nil. Wash and soak tuber well before cooking, but do not cut into the skin, even to remove imperfections or 'eyes'. Takes about 30 to 60 minutes to cook depending on coal heat. If not eating immediately, do not leave potatoes in foil wrapping. Unwrap and let surface dry
Do not remove husk. Soak corn before cooking. It takes about 10 to 20 minutes to cook depending on coal heat
Wash and soak cabbage. Drain excess water. Do not remove any dead leaves etc. Poke a knife halfway into the core from the top and pour in a little water (and meat fat for extra go). Can take up to 1 hour to fully cook
Large slabs work best. Reduce flesh loss by wrapping in edible leaves. If you don't like the charred bits, you can use Aluminium foil, or better yet a dutch oven. Time depends on mass and done-ness desired
Small goods like sausage (real meat and fat, not sawdust please) will have up to 5 mm of flesh loss, but are still fun to do.
Gut fish, but otherwise leave intact. Fish cooks relatively fast, time depends on mass. Pull sides apart and eat flesh directly off the skin and bone. If using a foil pouch you can add aromatics, raw sugar, and spices to make some amazing meals
Keep bananas in skin, make a couple of small cuts to let steam escape. Cooks in 10 to 15 minutes
Unpeeled and un-cored apples cook in 15 to 20 minutes (you can eat the core, it's good for you)
I believe the most accurate definition for this is "Pit Barbecue" although (as Ray points out) Kalua describes this technique as well, but I think as a 'general technique' Pit Barbecue is more accurate with Kalua being a "style" of Pit Barbecue.
This reminds me of Kalua a bit. In Kalua pork, a pig is wrapped in burlap and leaves and buried with hot embers and rocks under dirt and sand for hours.
Hangi is apparently somewhat similar as well.