Cover the mung beans with the water and refrigerate overnight. The next day, drain the beans and reserve the soaking water.
In a mixing bowl, combine the mung beans, rice flour, cumin seeds, green chile, asafoetida, cilantro, coconut, shredded carrot, and salt. Gradually add the water, mixing well with your hands to form a workable dough. Use only as much water as needed (about 1/2 cup).
Shape the dough into balls about the size of a tennis ball. Set aside. Flatten one portion of dough into a thin round.
Heat 2 tablespoons of vegetable oil in a griddle or skillet over medium heat. Place the rotti in the oil, and fry until golden brown, about 30 to 40 seconds. Flip the rotti over and fry until golden. Repeat with the remaining dough, adding 2 tablespoons of oil to the griddle for each rotti. Serve hot.