Take 1.5 cups of water in a pan, add the jaggery, allow to simmer over a medium flame till the jaggery dissolves completely. Give it an occasional stir, what you want is a jaggery syrup of about a 1-thread consistency.
Add the rice flour and 0.5 tbsp of ghee to the jaggery syrup, sprinkle 2 tbsp of toasted sesame seeds, give it a hearty mix, cook another 5 minutes or so.
Now switch off the flame, cover the pan, allow to rest for 10 minutes or so. If it is too dry, feel free to add a splash of warm water.
Mix well to form a soft dough.
Take a small portion of the dough, grease with a little ghee, gently shape into a 2.5 inch disc. Top with sesame seeds. Repeat for rest of the dough.
Heat the oil and 2 tbsp ghee in a pan over a low flame till just warm. (Take care to not over-heat the oil. If the oil is very hot, the outside of the pitha shall brown very quickly while the inside shall remain uncooked.)
Fry the pitha over a low flame till it fluffs up and gradually rises to the surface. Continue frying patiently till the pitha is gorgeous golden on all sides.
Serve at room temperature.