Wrap the cardamom pods in a newspaper and crush with a rolling pin. The seeds should not be crushed to a dust. The result should look somewhat like freshly cracked pepper. Discard the green skin of the pods.
In a small saucepan, heat 1½ cups of the milk over medium-low heat; do not bring to a boil, but keep warm while you prepare the kheer. In a large heavy-bottomed pan, add the remaining 3 cups of milk, the rice, crushed cardamom seeds, sugar and slivered almonds. Turn the heat to high. As soon as the milk starts to steam, turn the heat to low and cover with a lid.
Every 7 to 10 minutes, remove the lid and stir gently, from the bottom up, to ensure that the rice is not sticking to the base of the pan. After about 40 minutes, the milk should be thickened but not entirely absorbed. The pudding should have a soft, velvety consistency and not look congealed.
Taste the rice. If it seems undercooked, add some of the reserved warm milk, replace the lid and continue to cook for 7 to 10 minutes. When done, the basmati rice grains should be intact. Transfer the kheer to a container and allow it to come to room temperature before covering and refrigerating at least 5 hours, but preferably overnight, to set.