1. Pour water, yeast, sugar and vegetable oil into the mixer. Then, mix it a little bit, cover the lid and wait for 5 minutes.
2. At the same time, in the mixing bowl add bread flour, salt, sugar, vital wheat gluten, dough enhancer and mix it well.
3. After that, turn on the mixer in the lowest setting (#1) and slowly add the flour mixture from step 2. Then, cover the lid and change to a higher setting (#3) for 5 minutes until the dough is well mixed.
4. Take the dough out and put it in a big bowl. Cover it with a wet paper towel or damp cloth for 45 minutes to an hour at room temperature.
5. After that, the dough rises double in size.
6. Next, divide the dough evenly into 12 pieces.
7. Then, roll the dough like a rope, long and the ends are less thicker than the middle.
8. The following step, wrap the dough around the hot dog.
9. Continue step 8 and finish wrapping the rest of the dough. Then, put them on a tray with parchment paper. Cover with a damp cloth and wait for 30 minutes.
10. Meanwhile, beat an egg in a bowl.
11. After that, brush the beaten egg from step 10 on top of the hot dog buns.
12. Preheat the oven at 375 F and bake it for 15-18 minutes until it's golden brown.