In a medium saucepan, combine the arrowroot powder, milk, sugar, and salt. Stir well to dissolve the arrowroot powder completely.
Place the saucepan over medium heat. Continuously stir the mixture to prevent lumps from forming. Continue to cook, stirring constantly, until the pudding thickens and begins to bubble. This usually takes about 5-7 minutes.
Once the pudding has thickened, remove it from the heat. Stir in the vanilla extract. If using, add ground nutmeg or cinnamon for added flavor.
Transfer the pudding to serving dishes or bowls. Allow it to cool to room temperature, then refrigerate for at least 2 hours, or until fully chilled and set.
Enjoy your meal!