Make jaggery syrup: Heat water in a small bowl and add the jaggery. Stir until completely dissolved and cool down.
Make the batter: Add banana to a mixing bowl and mash it very well. Strain the jaggery syrup and add coconut, flour and soda. Whisk well adding more water as required to make a thick smooth lump-free batter of pouring consistency.
Fry Sweet Appam: Pour ¾ teaspoon ghee in each cavity and spread well to grease. When the ghee turns hot, pour batter with a tbsp to fill ¾ of the cavity. Let cook until the base is firm and set. Using a skewer or a wooden spoon, flip them and add more ghee as preferred.
Cook until golden, crisp and cooked through in the center. You may test by poking the appam in the center, the skewer should come out clean. Repeat cooking in batches, with the rest of the batter.