Start by soaking the red beans overnight or for at least 6 hours in water (Ibabad ang beans sa tubig). After soaking, drain and rinse the beans thoroughly. Cook them in fresh water for about 1 hour or until very tender. Process the cooked beans until smooth (hanggang maging malambot), then mix with sugar and cook down until it becomes a thick paste. Let the paste cool completely, then portion it into small balls and set aside.
Heat 1⅓ cups water with ¾ cup sugar until it reaches 180°F (82°C), stirring until the sugar completely dissolves. Gradually pour this hot liquid mixture into 3 cups of glutinous rice flour, mixing as you go. Knead the mixture until it becomes a smooth, pliable dough (masahan hanggang lumambot). Cover the dough and let it rest for 20-30 minutes.
After resting, divide the dough into 24 equal pieces. Take each piece and flatten it in your palm, place a portion of the cooled bean filling in the center, then carefully seal and roll into a smooth ball. Make sure there are no cracks or air pockets in the dough. Roll each sealed ball in sesame seeds (linga), pressing gently to ensure the seeds adhere well.
Heat oil in a heavy-bottom pot or wok (kawali) to 320°F (160°C). Carefully drop the sesame-coated balls into the oil. The temperature will naturally drop to around 300°F (149°C) - this is normal. Fry the buchi while constantly turning them for even cooking. As they cook, gradually increase the heat to finish at 350°F (177°C). The buchi are done when they float to the surface and turn golden brown.
Remove the cooked buchi using a spider strainer or slotted spoon and let them cool slightly before serving. They are best enjoyed hot or warm as merienda (afternoon snack). Any leftover buchi can be stored at room temperature for 1 day, in the refrigerator for up to 3 days, or frozen uncooked for up to 1 month. To reheat, place in a 375°F (190°C) oven for 2-3 minutes.