Place the golden raisins in a small bowl and add enough apple juice (or apple cider) to just cover. Set aside until ready to use. (Orange juice would be yummy, too, if you don’t want to use apple juice/cider.)
In a medium saucepan, bring the water to a full boil. Add rice, cinnamon stick(s), and ground cardamom. Stir well.
Place the lid onto the pot, lower the heat to low, and cook for 12 – 15 minutes, or until the liquid is absorbed and the rice is cooked.
Carefully remove the lid; it will be hot. Remove the cinnamon sticks with tongs; they have given their all.
Pour the 2 milks into the rice and stir, raising the heat to medium-high.
Bring the rice mixture to a gentle boil.
In another small bowl, scramble the egg and yolk with a fork or wire whisk.
Using a metal or plastic measuring cup, scoop about 1 cup of the liquid from the rice mixture. It is fine if rice gets included. Slowly pour the hot liquid into the eggs with one hand, while the other hand is whisking the liquid with the eggs in the bowl. (This is called “tempering.” It helps prevent scrambled eggs in your rice pudding. A very good thing!) Repeat with one more cup of liquid to the egg mixture.
Now, slowly pour the egg mixture back into the pot with one hand, while whisking it together with your other hand.
Maintain the medium-high heat. When the mixture is coming back to a boil, set your timer for 2 minutes. Whisk continually to allow the proteins in the eggs to create this thicker, creamy, dreamy, rich rice pudding. You want to see “blop blop” type of bubbles.
Drain the raisins well and fold them into the rice pudding along with the vanilla.
Pour the rice pudding into individual serving bowls and sprinkle with the ground cinnamon and ground cardamom, if you’d like. Serve warm.
Refrigerate any leftovers. When reheating leftovers, you may add a small amount of milk or half and half to thin the rice pudding; it will thicken as it cools. This dessert can be enjoyed cold, too.