Making Moong Dal Paste
Soak the moong dal or mung lentils, in enough water overnight or for 4 to 5 hours.
Drain and then grind the moong dal to a smooth paste with ¼ or ⅓ cup water to a smooth and fine consistency.

Making Moong Dal Halwa
Melt ghee in a nonstick kadai or frying pan or a well-seasoned wok or frying pan. Add the ground moong dal. Stir and mix well.

Keep on stirring the halwa on a medium-low to medium heat. The halwa has the raw aroma of the moong lentils and it should go away completely before you start with the next step. So till then you have to stir and cook the halwa.
The halwa first is pasty, then starts getting lumpy and then starts breaking down and getting separated with the fat releasing from the sides. Break the lumps while stirring.
Meanwhile when the halwa is cooking, in another pan or kadai, take milk, water and sugar.

Keep this pan on the stove top and stir so that the sugar dissolves. On a low or medium flame, heat this milk-water-sugar mixture till it comes to a boil.

The moong dal mixture should reach a granular consistency before you add the hot milk mixture. You should get a fried aroma from the mung lentils and the color should become golden. The fat also should get separated.
When the milk mixture comes to a boil, add it to the fried mung lentils.
The mixture sizzles, so be careful while adding the hot milk and water mixture.
Stir well. Simmer and cook stirring often.
The liquids should get absorbed and once again you will see the ghee getting separated.

Lastly add cardamom powder, chopped pistachios and kaju.
Serve Moong Dal Halwa hot. You can also garnish with some kaju, almond, pistachio.