Soak the dried mushrooms in the lukewarm water.
Place a pot of water, with a teaspoon of sugar and pinch of salt, over a medium-high heat and simmer the leeks until they soften. Drain the water.
Place a saucepan over a medium-high heat, melt half the butter, and sauté the rice and partially cooked leeks with the pinch of tarragon, salt and pepper.
Add the mushroom, the cognac and then slowly stir in the mushroom water.
Simmer the mixture for about 20 minutes until cooked.
Grate the cheese.
When ready, remove from the heat, stir in the remaining butter, add the grated cheese, and serve hot.
