|Heat the oil in a 3 quart saucepan and sauté the leeks for 1 minute, stirring frequently.
Stir in the rice, making sure to coat it thoroughly with the oil.
Stir in the mushrooms, Tarragon and salt. Reduce heat to medium and begin adding the stock, about 1/3 cup at a time, stirring constantly.
Just as the rice absorbs each addition of liquid, add another 1/3 cup stock.
Continue until the rice is almost done, about 30 minutes. Cook over medium heat, stirring constantly, until the rice achieves the desired consistency.
Serve in shallow soup bowls.