Grease a 9x13 inch baking pan and line it with parchment paper, leaving an overhang. Grease the parchment paper as well.
In a small bowl, sprinkle the gelatin over the 0.25 cup of cold water. Let it bloom for about 5-10 minutes.
In a medium saucepan, combine the 0.75 cup of water, granulated sugar, and corn syrup. Heat over medium heat, stirring until the sugar dissolves.
Bring the sugar mixture to a boil and cook, without stirring, until it reaches 240°F (115°C) on a candy thermometer. This usually takes about 8-10 minutes.
Once the syrup reaches temperature, remove it from the heat. Carefully stir in the bloomed gelatin until fully dissolved. Then, stir in the vanilla extract.
Using an electric mixer fitted with the whisk attachment, beat the mixture on medium-high speed until it thickens and becomes very fluffy, about 5-7 minutes. It should look like marshmallow creme.
Pour the marshmallow mixture into the prepared baking pan. Spread it evenly using a greased spatula.
In a small bowl, whisk together the powdered sugar and cornstarch. Lightly dust the top of the marshmallows with this mixture.
Let the marshmallows set at room temperature for at least 4 hours, or preferably overnight.
Once set, dust your hands and a knife with the powdered sugar and cornstarch mixture. Turn the marshmallows out onto a lightly dusted surface. Cut into desired shapes.
Dust the cut sides of the marshmallows with more of the powdered sugar and cornstarch mixture to prevent sticking.
Notes
Store homemade marshmallows in an airtight container at room temperature for up to 2 weeks. Enjoy them in hot cocoa, with s'mores, or as a sweet treat!