Heat about a 1 ½ cups of water and add the jaggery pieces to it. Let the jaggery melt and then turn off the flame and let the water cool down to room temperature.
In a large bowl, combine the flours, cardamom powder, dry ginger water and grated coconut and to this add the jaggery water. Mix it well and adjust the water to make it into a dosa batter consistency.
Heat a griddle or tawa and pour the prepared batter on to the tawa. Make a circle using the ladle by pushing the batter outwards. Add a little oil or ghee and cook the dosa. Flip it over and cook on the other side until the dosais are golden brown. Make sure that you cook the dosai in medium flame otherwise the jaggery will burn and become too brown.
Repeat with the rest of the batter and serve hot with butter!