Dissolve the brown sugar in 1/3 cup boiling water. Once the sugar is dissolved, add in 1/3 cup cold water to bring down the temperature.
In a large mixing bowl, add the rice flour and make a well in the center. Stir in the brown sugar water and stir to combine. Once combined, knead the dough in the bowl for 5 minutes and shape into a ball. Dough should be soft, pliable and smooth; add more flour or water if need be to adjust the consistency.
Roll the dough into a log, and then divide the log into 12 even pieces. Dust your hands with a little rice flour and form each piece into a ball roughly the size of a large walnut.
With the palm of your hands, flatten the dough balls into disks. Place 1/4 teaspoon red bean paste and a piece of banana in the center of each of the disks. Gather the sides toward the center and pinch close. Gently roll in the palms of your hands to reshape into a ball. Repeat with the remaining balls. Once all the balls are filled and formed, roll in the sesame seeds to coat thoroughly.
Heat 3 inches of oil in a pot or wok to 350 degrees F, or until a piece of dough browns in 15 seconds.
Deep-fry the sesame seed balls, a few at a time, until the sesame seeds are golden and the balls float to the surface, 3 to 4 minutes. Remove from the oil with a slotted spoon and drain on paper towels. Best served warm.