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Combine the gelatin and ½ cup cool water in the bowl of an electric mixer fitted with the whisk attachment. Set aside.
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Combine the sugar, corn syrup, salt, and ½ cup cool water in a small, deep saucepan.
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Cook the mixture over medium heat, stirring, until the sugar dissolves.
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Raise the heat to high and cook, without stirring, until the syrup reaches 240°F on a candy thermometer. Remove from the heat.
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With mixer on low speed, slowly pour the sugar syrup into the softened gelatin.
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Increase the speed to high, and whip until the mixture is very thick and fluffy, and has cooled to lukewarm, about 8 to 10 minutes.
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Sprinkle the bottom of a greased 9 x 13 pan with a handful of powdered sugar and approximately half of the crushed candy canes.
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Spread the marshmallow mixture into the pan.
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Use your wet hands to smooth and flatten the marshmallows.
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Sprinkle more crushed candy canes and powdered sugar over the top, and let sit for several hours before cutting.
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Use a greased knife or cookie cutters to make squares or other shapes.
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After cutting into shapes, dust the sticky, freshly cut edges of the marshmallows with powdered sugar and the remaining crushed candy canes.