Step 1: Prepare the Crust

1. In a large bowl, combine the flour, milk powder, salt, and sugar.

2. Cut in the softened butter until the mixture resembles coarse crumbs.

3. Add the egg and vanilla extract, then mix to form a smooth dough.

4. Wrap the dough in plastic wrap and refrigerate for 30 minutes.

Step 2: Preheat Oven and Prepare Tapioca

1. Preheat your oven to 350°F (175°C).

2. Soak tapioca pearls in water for about 30 minutes, then drain.

3. In a saucepan, combine soaked tapioca and milk over medium heat. Cook, stirring frequently until the pearls become translucent and the mixture thickens (about 15 minutes). Remove from heat.

Step 3: Make Tapioca Custard

1. In a mixing bowl, whisk eggs, sugar, cornstarch, and vanilla extract until smooth.

2. Slowly temper the egg mixture by adding hot tapioca milk mixture while whisking constantly.

3. Return the combined custard mixture to the saucepan and cook on low, stirring until thickened. Remove from heat.

Step 4: Assemble the Pudding

1. Roll out chilled dough and press it evenly into a greased baking dish.

2. Pour the tapioca custard over the crust.

Step 5: Apply Egg Wash and Bake

1. Brush the edges of the crust with beaten egg for a golden finish.

2. Bake in the preheated oven for 45-55 minutes until the custard is set and the crust is golden brown.

Step 6: Cool and Serve

Allow the pudding to cool before slicing. Serve warm or chilled as preferred.