Sprinkle 1 1/2 cups sugar evenly in a 10-inch cast-iron skillet; place over medium heat. Caramelize sugar by constantly stirring with a wooden spoon. Remove sugar from heat. Immediately coat sides and bottom of a heavily greased 3-quart baking dish with caramelized sugar. After cooling, rub with butter. Set aside.
Beat egg whites (at room temperature) until foamy. Gradually add 2 cups sugar, 1 tablespoon at a time, beating until stiff peaks form. Set aside.
Caramelize remaining 1/2 cup sugar; gradually add water, stirring well. Cook over medium heat, stirring often, until mixture reaches softball stage (240°). Slowly pour hot caramelized syrup over egg whites, beating 10 minutes at high speed of electric mixer. Pour egg white mixture into prepared dish. Place soufflé dish within a larger dish; fill outside dish with water about half way up sides of soufflé dish. Bake soufflé in this hot water bath at 300° for 1 hour. Invert onto a serving platter, and serve immediately.