In a medium saucepan, stir together granulated sugar and water. Bring to a boil over medium heat, stirring to dissolve sugar. Reduce heat to medium low, simmer 3 minutes. Remove from heat. Stir rum into hot syrup and set aside.
Combine whole wheat and rice flours in a medium sized bowl. Crush the cardamom pods, gather the seeds and discard the skin. Crush the seeds into a powder. Place brown sugar, salt, coconut, ginger, and cardamom in the carafe of a blender. Add just enough water - about 1/2 cup - to make blending possible and blend into a fairly smooth puree. Pour the puree into the flours and mix well with a wire whisk until smooth; add additional water as needed to make a moderately thick but pourable batter. Allow to rest covered for about 15 minutes to let the flours hydrate well.
Heat a skillet or griddle on low to medium heat. Grease and add a ladle full of batter, while spreading the batter in a circle. Cook dosa until each side is golden brown. Serve with warm rum syrup. Just a light drizzle to compliment them.