Preheat oven to 300°F.

Line a rimmed baking sheet with parchment paper.

Whisk egg white, 3 tablespoons sugar, 1/2 teaspoon vanilla extract, and a pinch of salt in a medium bowl.

Add 2 1/2 cups unsweetened coconut shavings and toss until evenly moistened.

Spread coconut mixture evenly on the prepared baking sheet.

Bake until coconut is light golden and beginning to crisp, stirring and turning frequently, about 22 minutes.

Cool on baking sheet.

Combine light coconut milk, regular coconut milk, 2/3 cup sugar, 2/3 cup unsweetened shredded coconut, 2/3 cup short-grain rice, and 3/4 teaspoon salt in a heavy large saucepan.

If using vanilla bean, scrape in seeds from the bean and add bean to the saucepan.

Bring the mixture to a simmer over medium heat, stirring occasionally.

Adjust heat so that the mixture is barely simmering; cover partially and cook until liquid is slightly translucent and pudding is thickened to the consistency of loose oatmeal, stirring and scraping bottom and sides of the pan frequently, about 45 minutes.

Remove vanilla bean, if using, or stir in vanilla extract.

Divide pudding among ten 3/4-cup ramekins or dessert glasses.

Sprinkle crispy coconut over puddings.

Serve warm or at room temperature.