Drain the soaked basmati rice completely. Transfer the rice to a blender or food processor and pulse until it is coarsely broken down, resembling fine semolina. Do not turn it into a smooth flour.

Pour the whole milk into a heavy-bottomed pot over medium heat and bring it to a gentle boil. Reduce the heat to medium-low and let it simmer for about 5 minutes, stirring occasionally.

Take 3 tablespoons of the warm milk from the pot and mix it with the ground rice in a small bowl to form a smooth slurry. Whisk this slurry steadily into the simmering milk to prevent lumps from forming.

Cook the mixture on medium-low heat for 15 to 20 minutes, stirring constantly with a spatula to prevent sticking at the bottom. The mixture is done when the rice grains are completely soft and the milk has thickened to a custard-like coating on the back of a spoon.

Add the sugar, cardamom powder, and half of the chopped nuts. Stir continuously for another 3 to 4 minutes until the sugar dissolves completely and the mixture thickens further. Turn off the heat and stir in the rose water.

Ladle the warm phirni into individual serving bowls or earthenware dishes. Garnish the top with the remaining slivered almonds and pistachios. Let them cool to room temperature, then place in the refrigerator for at least 2 hours until chilled and set.