Grease a 9x9-inch (23x23 cm) baking pan and dust it with a mixture of powdered sugar and cornstarch.
In a large mixing bowl, combine the gelatin with 1/2 cup of cold water. Let it sit for about 10 minutes to soften.
In a saucepan, combine the granulated sugar, corn syrup, 1/4 cup of water, and salt. Cook over medium heat, stirring until the sugar dissolves. Insert a candy thermometer and heat the mixture to 240°F (115°C). This is the soft-ball stage.
Carefully pour the hot sugar syrup into the softened gelatin, mixing continuously. Be cautious as the mixture will be extremely hot.
Using a hand mixer or a stand mixer, beat the mixture on high speed for about 10-15 minutes, or until it becomes thick and glossy. Add the vanilla extract during the last minute of mixing.
Quickly transfer the marshmallow mixture into your prepared baking pan, spreading it evenly. You can use a spatula dusted with powdered sugar and cornstarch to help with this step.
Let the marshmallows set at room temperature for at least 4 hours, or overnight for best results.
Once the marshmallows have set, dust a cutting board with the powdered sugar and cornstarch mixture. Carefully remove the marshmallow slab from the pan and place it on the board.
Use a sharp knife or cookie cutters to cut the marshmallows into your desired shapes and sizes. Make sure to coat the knife or cutters with the sugar-cornstarch mixture to prevent sticking.
Toss the cut marshmallows in the sugar-cornstarch mixture to coat all sides.
Your homemade marshmallows are now ready to enjoy! Store them in an airtight container at room temperature.