Grind the peanuts without letting them become powdery fine. They should just break up into smallish bits and chunks. Mix these with the sesame seeds.
Heat the ghee in a pan and add the jaggery and the water. Heat the mixture in to a thick syrup till it reaches the stage where a drop of it put in to a bowl of cold water will retain it's shape. This stage can take a while to reach so keep stirring the mixture every once in a while until then.
Take the pan off the heat now and stir in the cardamom powder and the sesame seeds and peanuts mixture. Mix thoroughly.
Cut through the mixture to make 4 equal parts, then apply some ghee on your hands and form equal sized balls (you should be able to make about 5 from each of those 4 portions). Place these on a plate that you would have greased with a little ghee already while the syrup cooked.
After they have cooled, the tilgud will acquire a yummy toffee-like texture. The tilgud will keep well for at least a few days in an air-tight container.