1, Rinse the beans in several changes of water. Drain the beans and put them into a bowl. Add enough water to cover by 1 inch. Set aside to soak for 6 to 9 hours.
2, Drain the beans and rinse them again. Put them into a saucepan with water to cover by 1 inch. Bring to a near boil over medium heat, and then lower the heat to a gentle simmer. Cover partially and cook for about 45 minutes, or until the beans are tender but not mushy. Let cool before using. Or, you may refrigerate them in their cooking liquid in a tightly covered container for up to 3 days.
3, To make the sugar syrup, in a small saucepan, whisk together the sugar and ⅔ cup of the water until combined. Bring to a boil over medium heat and boil for about 1 minute, or until the sugar dissolves and the mixture is clear. Let cool before using. There will be ¾ cup. Or, refrigerate in a tightly covered jar until needed.
4, Put the tapioca starch in a large bowl and make a well in the center. Bring the remaining ⅓ cup water to a boil, immediately pour it into the well, and stir with a wooden spoon or sturdy rubber spatula until the mixture is lumpy. Use your hand (it is not that hot) or a plastic dough scraper to gather the mixture into a rough mass. Turn it out, along with all the unincorporated bits, onto a large cutting board. Knead the dough vigorously for 2 to 3 minutes, pushing it with the heel of one hand and folding it over, to create a smooth, dense dough. The dough will seem dry at first, but as the water is absorbed throughout the mass, the dough becomes malleable like modeling clay. Work in a little more tapioca starch if the dough is sticky, or a few drops of water at a time if the dough is too firm. The finished dough will be slightly warm.
5, Cut the dough into 3 equal pieces. Roll out each piece into a strip 2 to 2½ inches wide and a scant ¼ inch thick. Allow the strips to cool, firm, and dry for 6 to 8 minutes, so they are easier to work with, flipping them midway so they dry evenly on both sides. Use a knife to cut the strips crosswise into short noodles a generous ⅛ inch thick. Pause occasionally to separate them with your fingers. They will be dry, which means they won’t stick together during cooking.
6, Set a bowl of cold water large enough to accommodate the noodles near the sink. Fill a 5-quart pot half full with water and bring to a rolling boil over high heat. Pick up the cutting board and scoot the noodles into the pot. Stir the noodles to prevent sticking. After the water returns to a boil, cook the noodles for about 5 minutes, or until they are coated with a clear layer of cooked tapioca. (They will look white in the pot, so use a slotted spoon to examine one.) Drain the noodles in a colander and immediately transfer them to the cold water bowl, where they will turn clear. Let the noodles cool before pouring off the water. (The noodles can be covered and kept at room temperature for about 4 hours. They lose their springiness if they are refrigerated. Cooled noodles stick together, so loosen and separate them with warm water before using.)
7, To serve, have ready 6 glasses; each should hold 1 to 1¼ cups. Drain the beans and divide them and the noodles evenly among the glasses. Add 2 tablespoons sugar syrup and about 3 tablespoons coconut sauce to each glass. Top with 2 to 4 tablespoons crushed ice, depending on everyone’s sweet tooth. Serve with spoons for stirring up the contents and eating.