Preheat in a deep frying pan 1 tablespoon of olive oil and add there the peeled and diced Jerusalem artichoke and water. Salt and pepper to taste. Cook over medium heat, stirring frequently, about 8 minutes or until the Jerusalem artichoke gets a golden hue, and put in a dish.
In the same frying pan add a tablespoon of butter and rosemary. Cook for about 2 minutes until the oil begins to brown. Then remove the frying pan from the fire, add the balsamic vinegar and mix the sauce well.
Now pour the prepared Jerusalem artichoke and serve it to the table.