Manually knead the sweet potato with the rice flour and refined flour, without using water. The dough should be soft and smooth. Cover for 15 min.
Make the stuffing by cooking the grated coconut and sugar together, until the sugar caramelises and the mixture becomes quite dry. Add the milk and cook for a few seconds. Remove into a bowl.
Make around 12 flattened discs out of the dough. Make an indent in the centre of each and add around ½ tsp of the sweet coconut stuffing. (This stuffing is called Narkeler Pur in Bengali.)
With the help of your palms, roll the flattened discs with the stuffiing, back into balls and flatten slightly.
Make the sugar syrup by boiling the water, sugar and the green cardamoms with the peels intact. Remove from the flame and keep aside.
Deep-fry each flattened Pithe in hot oil on a simmered-to-medium flame. Each Pithe should be uniformly golden-brown on both the sides.
Remove each Pithe from the hot oil and immerse into the hot sugar syrup for 20–30 min. Remove the Pithe into another container and sprinkle just little sugar syrup on the top of each Pithe.
The Pithe can be eaten after 30 min of resting in the sugar syrup and can be refrigerated for two days.