1. Prepare the Dough:

• In a large mixing bowl, combine the dry yeast, salt, and sugar.
• Add the lukewarm water and milk to the yeast mixture, stirring well. Let it sit for about 5 minutes until the yeast becomes frothy.
• Stir in the vegetable oil, melted butter, and egg white. Mix well.
• Gradually add the flour, mixing until a soft dough forms. Transfer the dough to a floured surface and knead for about 10 minutes, or until it becomes smooth and elastic.
• Place the dough in a greased bowl, cover it with a clean kitchen towel, and let it rise in a warm place for 1 hour, or until it doubles in size.

2. Prepare the Apple Filling:

• While the dough is rising, grate the apples into a bowl.
• Add a splash of lemon juice to prevent the apples from browning.
• Stir in the sugar, adjusting it based on the sweetness of the apples. Set the filling aside.

3. Shape the Buns:

• Once the dough has risen, punch it down to release the air.
• Divide the dough into 12-15 equal portions.
• Flatten each portion into a small circle using your hands or a rolling pin.
• Place a spoonful of the apple filling in the center of each dough circle.
• Fold the edges of the dough over the filling and pinch them together to seal, forming a bun.

4. Second Rise:

• Arrange the buns on a baking sheet lined with parchment paper, ensuring there’s enough space between them for expansion.
• Cover the buns with a kitchen towel and let them rise again for 30 minutes.

5. Prepare the Egg Wash:

• In a small bowl, whisk together the egg yolk and milk until smooth.

6. Bake the Buns:

• Preheat your oven to 375°F (190°C).
• Brush the tops of the risen buns with the egg wash to achieve a shiny, golden crust.
• Bake for 20-25 minutes, or until the buns are golden brown and sound hollow when tapped.

7. Cool and Serve:

• Transfer the baked buns to a wire rack and let them cool slightly.
• Serve warm or at room temperature and enjoy the soft, fluffy texture and sweet apple filling.