Soak 20 almonds, 10 cashews, and 15 pistachios in water for 4 hours. Soak 1½ tablespoons of melon seeds and 1½ tablespoons of poppy seeds in a separate bowl of water.
Drain the nuts and seeds and peel the almonds. Grind them to a smooth paste with 1½ tablespoons of fennel seeds, 12 green cardamom pods, 1 piece of cinnamon stick (1in / 2.5cm), 4 black peppercorns, and ½ cup of milk.
Bring 4 cups of milk to a gentle boil. Stir in 5 tablespoons of sugar and the paste, then turn off the heat.
Refrigerate for at least 4 hours, then strain. Divide 4 teaspoons of gulkand (rose petal preserve) among glasses, pour in the thandai, and garnish with sliced nuts.