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Generously butter a 9-by-13 inch cake pan. Sift the cornstarch with the confectioners' sugar and set half aside. Add the remaining mixture to the pan and shake to coat; tap the excess out onto wax paper and sift it back into the pan.
In a small bowl, soften the gelatin in 1/2 cup of the water. In a medium saucepan, boil the remaining 1 cup of water with the sugar and corn syrup until the syrup reaches 245° on a candy thermometer; remove from the heat. Add the gelatin mixture and stir until dissolved.
In a standing mixer, beat the egg whites until soft peaks form. At medium speed, beat in the hot syrup in a thin stream. Increase the speed to medium-high and beat until cooled to room temperature, about 10 minutes. Beat in the rose water and vanilla. Spread the marshmallow in the prepared pan and let stand until set, at least 2 hours.
Run a thin knife around the marshmallow. Generously sift some of the reserved cornstarch mixture on top. Cover with a cutting board and invert, then tap on the pan to release the marshmallow. Using a moistened sharp knife, cut the marshmallow into 1-inch pieces. Cover a large board with wax paper and dust with more cornstarch. Coat each marshmallow with the cornstarch, then transfer to wax paper to set.