In a heavy saucepan combine sugar and water. Bring the liquid to a boil over low heat, swirling the syrup and washing down any sugar crystals clinging to the sides of the pan with a brush dipped in cold water. Boil the syrup until it reaches the softball stage, or until a candy thermometer registers 240 degrees F.
While the syrup is cooking, in the bowl of an electric mixer, beat egg whites until they are foamy. Add cream of tartar and a pinch of salt and beat the whites for 30 seconds. Sprinkle in sugar and beat the whites until they hold stiff peaks. Add the syrup in a stream, beating, and beat the meringue for 10 minutes, or until it is cool. Fill a pastry bag fitted with a 1/3-inch plain tip with the meringue and pipe out 66 mounds, each about 1-inch in diameter, onto a large baking sheet lined with parchment paper to make mushroom caps. Hold the pastry bag straight up and pipe out 66 cones on to the baking sheet to make mushroom stems. Bake the meringues in a preheated very slow oven (200 degrees F) for 1 hour. Remove the baking sheet from the oven and push in the undersides of the mushroom caps. Return the meringues to the oven and bake them for 30 minutes more. After the 30 minutes, turn off the heat and let the meringues stand in the oven for 2 hours more.
Fill a pastry bag fitted with a small star tip with a creme ganache and pipe the cream into the undersides of the caps to simulate gills. Push a stem into each cap, stand the mushrooms upright on their stems in a shallow dish, and set them aside until the creme ganache is firm. Store the mushrooms covered.
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