In a wok or deep-sided, heavy saucepan, pre-heat the oil for deep-frying to 350 degrees F. Make sure that there is at least 3 inches of oil in the wok. Spread the sesame seeds over a piece of wax or parchment paper. Place a small bowl of water beside the sesame seeds.
Dissolve the brown sugar in 1 cup of the boiling water.
Place the rice flour in a large bowl. Make a "well" in the middle of the bowl and add the dissolved sugar and water mixture. Stir until you have a sticky, caramel-colored dough, adding as much of the remaining 1/3 cup of boiling water as needed (don't add the water if not needed).
Pinch off a piece of dough roughly the size of an average golf ball (about 1 tablespoon).
Push your thumb into the dough to make an indentation. Roll 1 level teaspoon of sweet red bean paste into a ball. Place the red bean paste in the hole, and shape the dough over the top to seal. Make sure the red bean paste is completely covered. Continue with the remainder of the dough.
Dip a ball into the small bowl of water (this will help the sesame seeds stick to the ball). Roll the ball over the sesame seeds. Repeat the process with the remainder of the balls. Deep-fry the sesame seed balls, a few at a time, in the hot oil.
Once the sesame seeds turn light brown (about 2 minutes), use the back of a spatula or a large ladle to gently press the balls against the side of the wok or saucepan. Continue applying pressure as the balls turn golden brown and expand to approximately 3 times their normal size.
Drain the deep-fried sesame seed balls on paper towels. Serve warm. If preparing ahead, refrigerate and then re-heat the balls until they puff up again.