Soak the agar-agar in cold water - right in the saucepan you'll use to cook the syrup.
Put the banana pulp in a pot with 150 g of sugar, mash with a fork, and blend until smooth. Set the puree on the stove, bring to a boil, and cook for a couple of minutes.
Remove from heat and press the puree through a sieve straight into the bowl you'll use to whip the marshmallow mixture. Put the bowl of puree in the freezer for 10 minutes to cool.
Put the soaked agar on the stove and bring to a boil. Add the remaining 210 g of sugar and cook the syrup for 5-7 minutes - until it thickens and forms threads off a spoon that set instantly. At the same time, whip the banana puree with half the egg white for a couple of minutes, then add the second half and whip until the mixture increases in volume.
Take the finished syrup off the heat and pour it in a thin stream into the whipping banana-and-egg-white mixture, whipping for another couple of minutes - the mixture will increase dramatically in volume and start to set.
Immediately transfer the mixture to a piping bag and pipe the marshmallow shapes onto parchment.
Leave the shapes to dry at room temperature for a full day, then roll in powdered sugar and join the halves together. Enjoy!