Wash, peel and cut roughly the carrots. Grind with very little water to a smooth paste. Measure 1/4 cup and set aside.
Mix besan with oil with a whisk to a smooth paste. Keep a greased tray ready.
In a heavy bottomed vessel, take carrot puree, sugar and 1/4 cup water. Start heating.
Mix well and bring to boil. Let it come to one string consistency. keep the flame low while nearing the consistency. Check a little of the syrup between your thumb and forefinger, a long string forms in between. Add the besan paste and mix well.
Pour in the ghee in 3-4 parts in regular intervals, while you keep stirring.
At one stage, the whole mixture turns pale, a pleasant besan smell wafts and becomes frothy, leaving the sides of the pan.
Pour immediately to the tray. Let it set for 5 mins. Cut into Mysore pak when it is still warm. Let it cool completely before you try to take out.