Bring rice and 2 cups milk to a boil in a saucepan. Reduce heat to medium-low, cover, and simmer until the rice is tender and the liquid has been absorbed, 20 to 25 minutes.
Mash rice with a spatula or in a blender until smooth.
Add remaining 2 cups milk and cook until thick, about 10 more minutes. Stir sugar into rice pudding.
Slowly mix ghee into rice pudding, keeping the saucepan over medium-low heat, until pudding no longer sticks to sides of pan, about 5 minutes.