In a big bowl, stir together bread flour, cake flour, and salt. Set aside.
In a medium bowl, combine warm milk, butter, sugar, and yeast until the butter and sugar are fully melted.
Pour the milk mixture and egg into the flour. Stir together until dough forms.
Using hands or dough hook, knead the dough until smooth and elastic, but still soft. It takes about 10-12 minutes by hands or 8-10 minutes in a stand mixer.
Form dough into a ball. Put the dough into a lightly oiled large bowl. Cover with a clean kitchen towel and let the dough rest and double for 60-90 minutes at warm temperature.
Curry Filling
While waiting for the dough to rise, make the curry filling. Heat oil in a frying pan over medium-high heat. Add onion, stirring until softened. Add potatoes and carrot, cook for 5 minutes or until the potatoes and carrot are fully cooked.
Add ground beef and break it down into small pieces with a wooden spoon. Cook for 5 minutes or until browned. Add soy sauce, ketchup, and curry roux. Break down the curry roux into small pieces with a wooden spoon.
Mix water and cornstarch to make a slurry. Pour the slurry into the frying pan. Stir together until everything is well combined and thickened. Turn off the heat and set aside.
Assemble
After the dough has doubled, punch down the dough. Transfer it to a lightly floured surface and knead the dough to release the gas.
Measure the weight of the dough and filling with a kitchen scale and divide into 16. Cut the dough into 16 and roll them into balls. Create a smooth surface by pulling all the sides of the ball to the bottom and pinch them together.
Roll a ball of dough with a rolling pin into rounds about 10 cm/4-inch across. Flatten out the edges a little, so that the seam will not be too thick and doughy. Place the filling into the center of the round dough and gather the edges to cover the filling. Pinch the dough to close any seam.
Prepare two shallow dishes and put beaten egg and breadcrumbs separately. Drop the dough into the beaten egg, then lay it in the breadcrumbs. Turn it over and press the breadcrumbs to coat. Set aside.
Put the breaded dough a large baking pan. Cover with a clean kitchen towel and let the dough rest and double for 20-30 minutes at warm temperature until they puff up a bit.
When the oil is heated to 350F/180°C, carefully drop in curry bread in several batches into the oil. Keep turning them while they deep fry. Cook until golden brown for about 4-5 minutes. Transfer to the wire rack or paper towel to drain while it cools. Serve warm.