Heat the ghee in a heavy-bottomed pan over medium heat; fry the cashews in the ghee until golden brown, about 5 minutes. Scrape onto a chopping board to cool, leaving some of the ghee in the pan and return the pan to the stove. When the cashews are cool, chop coarsely.
Mix the milk, sugar and semolina into the ghee remaining in the pan. Bring the mixture to the boil; reduce heat to low and cook, stirring frequently, until the mixture becomes very thick, 30 to 45 minutes. Stir the cardamom into the mixture.
Lightly grease a rimmed dish. Pour the milk mixture onto the prepared dish and spread into an even layer. Sprinkle the chopped cashews over the mixture. Score the mithai into squares and allow to cool completely before cutting.