In a small saucepan, combine sugar and water. Heat over high heat, brushing down sides of pot as necessary with a pastry brush dipped in water. Cook until sugar syrup registers 240°F on a candy thermometer (soft ball stage).
Meanwhile, combine egg whites and cream of tartar in the bowl of a stand mixer fitted with a whisk attachment. Set mixer to medium speed and mix until soft peaks form, about 2 minutes.
With the mixer running, carefully and slowly drizzle in hot sugar syrup. Increase speed to high and whip until desired stiffness is achieved.
To prepare the Meringue Mushrooms:
Prepare the Italian Meringue as above; pipe mushroom tops and bottoms as demonstrated. Place in a warm, turned off oven, and leave overnight.