In a bowl, whisk together the Eggs, egg yolk, sugar, cornstarch, and cake flour until smooth.

Heat the milk in a saucepan, and temper the egg mixture with half of it.

Cook over medium heat until thickened, stirring continuously.

Stir in butter and vanilla; chill the custard in the refrigerator.

In a large mixing bowl, combine bread flour, sugar, condensed milk, cold milk, cold water, and half the whisked egg, followed by the instant yeast.

Mix until combined, then knead the dough for about 5-7 minutes until smooth.

Let it rest for 30 minutes covered with a damp cloth.

Add the sea salt and softened butter to the rested dough.

Knead for an additional 5-10 minutes until the dough is silky and elastic.

Place in a lightly greased bowl, cover, and let it rise in a warm, draft-free area for 1 to 1.5 hours or until it doubles in size.

Once risen, punch down the dough gently to release air.

Divide it into 8 equal pieces.

Shape each piece into a ball, roll it flat, and fill it with a generous spoonful of custard.

Seal the edges tightly for round buns or fold over for a semi-circle shape.

Place the shaped buns on a baking tray lined with parchment paper.

Cover them lightly and let them proof for about an hour until they puff up a bit and become airy.

Preheat your oven to 375°F (190°C).

Brush the tops of the buns with the remaining whisked egg for a beautiful golden finish.

Bake for 12-14 minutes or until light golden brown.

Once baked, transfer the buns to a wire rack for cooling.

Let them rest for about 10 minutes before serving—enjoy them warm for the best experience!

Optional: Drizzle with leftover custard for an extra touch of sweetness!