Line a 20-cm (8-inch) square dish with plastic wrap and oil lightly.
In a large bowl, sift the sugar and cornstarch together. Set aside.
In a saucepan, sprinkle the gelatin on the strawberry purée. Let soften for 5 minutes. Add the sugar and bring to a boil, stirring to dissolve the gelatin. Remove from the heat and transfer to a bowl. Let cool for 5 minutes.
Set the bowl over a saucepan partially filled with cold water; the water should touch the bottom of the bowl. Beat with an electric mixer until the mixture has cooled to room temperature and forms stiff peaks, 5 to 7 minutes (or about 15 minutes if the mixture is not whipped over cold water). Spread evenly in the dish and refrigerate until thoroughly chilled, about 3 hours.
Lightly dust a clean surface with the icing sugar mixture. Unmould the marshmallow and remove the plastic wrap. Using a knife with a lightly moistened blade, cut the marshmallow into 4-cm (1 1/2-inch) squares. Roll each square in the icing sugar mixture, shaking off any excess. Place the marshmallows on a cookie sheet and let warm to room temperature. If necessary, roll a second time in the icing sugar mixture.
The marshmallows can be stored for several days in an airtight container at room temperature.
Recipes with the "Healthy Pick" stamp have been evaluated by a registered dietitian member of the Ordre professionnel des diététistes du Québec.