Grease a 9x9-inch baking pan with cooking spray and set aside.
Combine the Dutch-process cocoa, espresso powder, and ⅓ cup boiling water in a small bowl. Whisk until smooth (should be the texture of a ganache or a thick icing). Set aside to cool.
In the bowl of a stand mixer, add ⅔ cup cold water. Sprinkle gelatin on top and let bloom.
In a medium saucepan over medium-high heat, combine granulated sugar, corn syrup and ⅓ cup water. Stir until sugar is dissolved. Bring the mixture to a boil, swirling the pan occasionally, until the mixture reaches exactly 240°F on a candy thermometer, about 10-12 minutes. Immediately remove from heat.
Add the chocolate mixture to the bloomed gelatin in the bowl of the stand mixer. Mix briefly to combine.
With the stand mixer on low speed, slowly and carefully pour the melted sugar mixture into the stand mixer. Add the vanilla extract and salt.
Slowly (to avoid splashes) increase the speed to high. This is also a great time to use a splash guard for your stand mixer, if you have one! Whip until the mixture is stiff and lightened in color, about 12-14 minutes. When you remove the whisk, stiff threads should form that take a few seconds to fall back into the marshmallow mixture. Working quickly, pour the mixture into the prepared baking pan and use a spatula to help spread evenly.
Let the marshmallows sit and firm for at least 4 hours at room temperature or 2 hours in the refrigerator.
In a small bowl, whisk together ¼ cup powdered sugar and ¼ cup Dutch-process cocoa powder for coating the marshmallows.
Lightly dust your work surface with the powdered sugar mixture. Use a butter knife to slice around the edges of the pan, then turn the marshmallow out onto the work surface. You may need to pry it out at a corner. Use a sharp knife to cut the marshmallow into 16 pieces. If needed, spray the knife with cooking spray to help prevent sticking. If there is excess cooking spray on your marshmallow, dab with a paper towel to remove.
Roll each marshmallow in the powdered sugar mixture on each side to prevent sticking, then serve.
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Notes
Corn syrup substitute: You can use honey or agave nectar as a 1:1 substitute for the corn syrup. Gelatin substitute: Unfortunately, there is not an easy substitute for gelatin. Agar agar does not work in a 1:1 substitute.