Combine the mung beans and 1 cup water in a pot and bring to a boil; boil over medium heat until the beans are very tender, about 30 minutes. Mash the beans thoroughly. Stir 1/2 cup sugar into the mashed beans; set aside.
Mix the glutinous rice flour, 2 tablespoons sugar, salt, and 1/4 cup water together in a large bowl; knead together just enough to form a ball. Divide the ball into small pieces and roll into balls. Flatten each ball of dough, and spoon 1 tablespoon of the mashed bean mixture into the middle of the dough. Wrap the dough around the bean mixture and pinch the edges together to seal. Repeat until all the dough and paste is used.
Heat oil in a deep-fryer or large saucepan to 350 degrees F (175 degrees C).
Fry the balls in batches in the hot oil until golden brown, 5 to 10 minutes per batch. Serve hot.