Dough
Combine flour, sugar, salt, and yeast in a large bowl. Add egg and warm milk. Mix until it becomes a dough.
Transfer the dough onto a work surface. Lightly flour if you find the dough too sticky to handle. Knead for 2 minutes.
Wrap and knead the softened butter into the dough until fully incorporated. It will be messy at first but as long as we keep kneading, the dough will become less greasy and easier to handle. Knead for 10 minutes or until it becomes smooth, elastic, and not sticky.

Shape into a dough ball. Grease it with some vegetable oil in a large bowl. Cover the bowl and place it in a warm area until the dough is doubled in size (about 1 hour).
Custard filling
In a saucepan, whisk together egg, sugar, and milk. Sieve in cornstarch and flour. Whisk again to completely dissolve them.
Cook the mixture over low heat and whisk it constantly until thickened.

Turn off the heat and whisk in vanilla. Transfer custard into a small bowl. Cover its surface with plastic wrap to prevent a crust from forming. Set aside to cool (refrigerate if you're not using it in the next hour).
Assembly
Grease a 20cm (8-inch) round pan with butter or non-stick cooking spray. Line the bottom with parchment paper.

Punch down the dough to release the air inside, then transfer onto a work surface. Divide it evenly into 5 pieces. Shape each piece into a ball and set them aside for 15 minutes with a cover.
Using a rolling pin, roll out each piece into an elongated shape (about 25cm long). Press down the dough around the edges with your thumbs to keep it from stretching back.

Cut out thin strips of dough along the top 2/5 part of the dough (lengthwise), but keep them intact with the remaining part of the dough. The strips will be dangling if we pick up the whole dough. Spread a thin layer of custard filling over the remaining part
Fold 1/4-inch (1 cm) from three of the dough edges over the custard. Then start rolling towards the dough strips from the opposite end to form a log. Repeat with the other 4 pieces to get a total of 5 logs.

Place dough logs around the perimeter of the prepared pan. Cover and rest it in a warm area for 1 hour.
Gently brush the dough with milk or egg wash. Bake in a preheated oven at 340°F (170°C) for 25 minutes or until golden brown. Cool completely on a wire rack