Liberally grease a 9 x 13-inch baking dish. Whisk together the powdered sugar and cornstarch in a small bowl and then dust the greased dish all over with the mixture.
You want the bottom and all sides of the dish well and evenly coated.
For the Marshmallows:
To the bowl of a stand mixer fitted with the whisk attachment, add ½ cup of the cold water and sprinkle the gelatin over the top. Allow to sit, undisturbed, for 10 minutes. This allows the gelatin to “bloom.”
Meanwhile, in a large saucepan fitted with a candy thermometer, combine the granulated sugar, corn syrup, salt, and remaining ¼ cup cold water.
Heat the mixture over medium-high heat, stirring to help the sugar dissolve.
Bring the mixture to a boil and cook until the thermometer reads 240°F, about 1-2 minutes.
Turn the stand mixer on the lowest speed and VERY CAREFULLY and slowly stream in the hot sugar mixture to the gelatin mixture in the bowl.
Once all of the hot sugar mixture has been added and somewhat incorporated, gradually increase the speed of your mixer to high.
Beat on high for 5 minutes, or until the mixture has started to grow in volume. Stop the mixer and add in the chai spice and vanilla bean paste/extract.
Continue beating the mixture on high for another 5-7 minutes or until it has doubled in volume, is glossy and white, and can hold stiff peaks.
Grease a spatula and use it to help pour the mixture from the bowl into the prepared baking dish. Smooth out the top as much as possible with the greased spatula.
Dust the top of the marshmallow mixture with a tiny bit of powdered sugar and then lightly cover the dish with plastic wrap.
Allow the marshmallows to sit at room temperature for 3-4 hours, or until they are set and firm (a little jiggle is good!).
Dip a sharp knife in powdered sugar and run it around the edges of the pan. Carefully invert the marshmallows onto a surface dusted with powdered sugar. Use the knife to slice the marshmallow into squares.
If your marshmallows are excessively sticky, dust them lightly with powdered sugar. Leftover marshmallows can sit at room temperature, well wrapped, for up to a week.
For the Hot Chocolate:
Once your marshmallows are ready and cut, start making your hot chocolate by combining the milk and sugar in a medium saucepan.
Place the pot over medium heat and whisk until the sugar dissolves.
Meanwhile, place the chopped chocolate in a heat-safe bowl and microwave on LOW in 20-second increments, stirring after each session, until it is melted and smooth.
Once the milk is hot but not boiling, whisk the melted chocolate into the pot. Keep stirring until everything is smooth and creamy and well mixed. Add the salt and vanilla and whisk to combine.
Pour into mugs and garnish with the chai marshmallows and a dusting of chai spice.