I just wrote about a three-century-old dango place, but here's another one that's over 1,000 years old! They literally only sell one item, aburi mochi which are an old-fashioned Japanese treat made by taking sticky and pounded glutinous rice covered with kinako toasted soybean flour and broiling it over a charcoal fire on bamboo skewers. They haven't changed the recipe since they started over 1000 years ago!!
The mochi comes with tea and is served with a slightly sweet miso paste.