Add the flour to a bowl. Sprinkle in the salt, add the ghee and 2 tbsp oil. Mix well till the ghee is well incorporated into the flour.
Make a well in the flour, add 1/4 cup of warm water. Gently mix the water and flour and start kneading with your fingers.
Gradually add more warm water as needed till the dough becomes firm but soft and pliable when rolled. Cover with a wet or damp cloth for 10 minutes.
In another small bowl, crumble the kanchagolla. Keep aside.
Divide the dough into small balls, using a rolling pin, roll out each dough ball to a flat circle of about 3 inches in diameter.
Add 1.5 tsp of kanchagolla in the middle of a circle, cover with another flat circle and carefully press the edges together.
Use your fingers or a fork to crimp the dough along the edges as shown in the image. Repeat the same for the rest.
Heat oil in a deep-bottomed pan, deep fry till golden brown. Keep aside on a kitchen absorbent towel.
Pour the milk into a heavy bottomed saucepan, simmer over a low flame till the milk reduces to almost one third in volume.
Once the milk has reduced, add the 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 !!)
Gently add the kanchagolla-stuffed luchis one by one into the milk. Cook over a medium flame for about 3-4 mins. Carefully stir the milk a couple of times in between.
Allow to cool and serve.