The fire is the most important part. The cook (called the 'asador') lights a wood fire early - sometimes two or three hours before the food goes on. The wood burns down to glowing coals, and only then is the meat slowly grilled over them. Slow cooking, slow eating, slow company.
An asado is shared work. Someone brings the bread. Someone makes a green sauce called chimichurri - made from parsley, garlic, oil and a splash of vinegar - to drizzle on everything. Someone sets the long table. Children run around. Mate gets passed in a circle. Nobody is in a hurry.
The traditional grill is called a 'parrilla'. It is a flat metal rack over the coals, and good ones have a handle to raise and lower the meat - higher for slower, gentler cooking, lower for a quick char. Many Uruguayan houses have a parrilla built right into the kitchen wall or a corner of the garden.
Asado isn't only meat. Vegetables go on the parrilla too - whole peppers, onions, sweet potatoes. A famous Uruguayan dish made on the parrilla is 'provoleta' - a thick slice of melty cheese cooked until it bubbles. Vegetarian families have their own asado with grilled vegetables and provoleta. The point is the company, the fire and the time.

