Bring tapioca, coconut milk, and salt to a boil in a saucepan over medium-high heat, stirring constantly. Reduce heat to medium-low and simmer for 5 minutes. Stir in sugar until dissolved.

Beat egg in a medium bowl until smooth. Whisk in about 1/2 cup hot tapioca mixture, 1 tablespoon at a time, then scrape egg mixture into tapioca mixture; stir. Simmer gently until pudding is thickened, 3 to 5 minutes. Remove from heat and allow to cool for 10 minutes.

Stir in vanilla until incorporated. Serve warm or chilled.