Gather and measure all the ingredients. If using freshly cooked rice, allow it to cool slightly and break up any clumps with a fork.

Place the cooked rice in a medium saucepan. Add 1 1/2 cups of milk and the salt, stirring until combined.

Cook over medium heat for 15–20 minutes, stirring frequently, until the rice mixture becomes thick and creamy. Adjust the heat as necessary to prevent the milk from scorching.

In a small mixing bowl, whisk together the beaten egg, granulated sugar, and remaining 1/2 cup of milk until smooth and well combined.

Gradually add a few spoonfuls of the warm rice mixture to the egg mixture while whisking continuously. This tempers the egg and helps prevent it from scrambling.

Slowly pour the tempered egg mixture back into the saucepan, stirring gently. Add the golden raisins, if using, and mix until evenly distributed.

Continue cooking over medium-low heat for 2–3 minutes, stirring continuously, until the pudding thickens and reaches an internal temperature of 160°F (71°C). Avoid boiling.

Remove the saucepan from the heat. Stir in the butter and vanilla extract until the butter melts and the pudding becomes smooth and creamy.

Spoon the rice pudding into individual serving bowls. Sprinkle with ground cinnamon or nutmeg, if desired, and serve warm or chilled.