Dust the bottom of an 8"x 8" pan with powdered sugar and set aside.
Make your fluffy aquafaba
Put the aquafaba in a mixing bowl with the cream of tartar and mix on high for 6 minutes until very fluffy.
Add some vanilla extract and whip for 3 more minutes until it is white again and it forms very stiff peaks. (You need to whip the aquafaba for a total of at least 9 minutes.)
Make your agar agar syrup
In a small saucepan, combine water and agar agar and bring to a boil.
Boil the water and agar agar for 3 minutes stirring frequently.
Add sugar and boil for another 3 minutes stirring constantly over medium-low heat. (Be careful not to cook it too hot or you will burn or caramelize the sugar.)
Mix everything together
Turn off the heat and add the hot sugar mixture into the beaten aquafaba.
Add this mixture slowly while beating aquafaba with a mixer set to low for about 30 seconds. This will turn the fluffy white mixture a little shiny.
Quickly pour it into the pan that has been dusted with powdered sugar.
Cooling and drying your marshmallows
Dust the top of the marshmallows with powdered sugar and let sit and cool for at least an hour.
Cut into 1" squares and dust all sides with powdered sugar.
Turn your oven to 150°F (66°C). Once it reaches that temperature, turn it off and set your cubed marshmallows in the warm oven for about an hour to dry out a little.
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Notes
Whip the aquafaba for a full 9 minutes before adding the agar agar syrup.
Stir the agar agar mixture constantly over medium-low heat, just hot enough to keep it slowly bubbling.
Make sure to cook the agar agar for a total of 6 minutes to make sure it's completely dissolved and melted.
Be sure to add all of the agar agar syrup to the aquafaba! Use a rubber spatula to scrape out the bottom of the saucepan to get it all.
Immediately pour the marshmallow mixture into the pan while it's still hot. (Once it cools, it will set and become firm in whatever position it's in).
Wait a full hour before cutting into squares.
Make sure to turn your oven off before putting the marshmallows into it. You don't want to melt them, just dry them out a little.