Mix the grated coconut and jaggery in a pan, cook over a low flame, stirring occasionally. Till the jaggery is well incorporated into the coconut and it turns a bit sticky. 7-10 odd minutes I would reckon. Remove from heat.
Take a pan, add 1 cup of water and bring to a boil. Add 2 tsp ghee, lower the flame, add the semolina to the boiling water, stirring continuously to form a thick batter. Keep stirring the batter to prevent lumps from forming. Continue to cook till the semolina is cooked and the batter has turned into a soft dough.
Allow the dough to cool just enough for you to handle, shape into small balls, keep aside.
Now take a dough ball on your palm, press it gently in the middle using your thumb forming a small oval cup. Place a small portion of the coconut-jaggery mixture in the middle of the cup.
Very gently bring the edges of the dough cup together to cover the stuffing. Press the edges gently with the back of a fork. Repeat for the rest of the dough.
Pour the milk into a heavy bottomed saucepan, let it simmer over a low flame till it reduces to little more than one third in volume. Stir frequently.
Gently add the dumplings one by one into the milk. Cook over a low flame for about 10-12 mins. Stir the milk very carefully a couple of times in between.
Lower the flame, add the remaining grated jaggery. Give it a hearty stir, continue to cook till the jaggery has melted. (If you like it sweeter, feel free to indulge - add some more grated jaggery !!)
Allow to cool to room temperature and serve.