Crush 10 of the cardamom pods, transferring the seeds to a mortar and pestle; reserve the other 6 pods. Grind the seeds into a fine powder and set aside.
In a medium saucepan, combine the 6 reserved cardamom shells with the water and sugar, then bring to a boil. Once boiling, reduce the heat to low.
Meanwhile, in a 6-quart Dutch oven or wok, melt the ghee and the 6 remaining cardamom pods over medium-high heat. Reduce the heat to medium and add the semolina. Cook, stirring constantly until toasted, 3 to 4 minutes. Add the almonds, raisins and salt, and stir until the almonds are golden, 1 to 2 minutes.
Skim the cardamom shells from the simmering water and slowly add to the semolina, stirring constantly. Cook until the pudding is thick and the semolina is tender, 3 to 4 minutes.
Divide the pudding between bowls and garnish each with a spoonful of crème fraîche and the reserved cardamom powder, then serve.