Combine rice, milk, and water in a medium saucepan over medium heat. Bring to a gentle simmer, stirring frequently.
Reduce heat to medium-low. Simmer for about 15 minutes, stirring every couple of minutes, until the rice begins to soften and the liquid starts to thicken.
Stir in the applesauce, brown sugar, cinnamon, cardamom (if using), and salt. Mix well to combine.
Continue simmering on medium-low for another 10-15 minutes, stirring frequently, until the rice is fully tender and the pudding is thick and creamy.
Remove from heat. Stir in the vanilla extract and butter (if using). The pudding will thicken more as it cools.
Serve warm with your favorite toppings, or chill in the fridge and enjoy cold.
Notes
Stir frequently: Milk and rice stick to the bottom fast. Keep stirring, especially in the last 10 minutes.
It thickens as it cools: Take it off the heat when slightly thinner than desired. Add a splash of milk when reheating.
Leftover rice shortcut: Use 1 ½ cups cooked rice, reduce milk to 1 ½ cups, skip the water. Simmer 10-12 minutes with applesauce and spices.
Dairy-free: Use oat milk or coconut milk and skip the butter.
Storage: Refrigerate in an airtight container for up to 3-4 days. Reheat on stovetop with a splash of milk.