Soften the butter until it can be easily pressed with a finger, then set it aside. Add all ingredients except the salt and butter into the bread machine pan: bread flour, sugar, milk, egg, and yeast.

Place the pan into the bread machine and start the kneading function. Let it knead for 20 minutes until the dough becomes mostly smooth and can stretch into a thicker membrane.

Add the salt and softened butter. Restart the kneading function and continue kneading for another 20 minutes, until the butter is fully absorbed and the dough can stretch into a thin, elastic windowpane. The membrane should be strong and not tear easily — this step is crucial for soft buns.

Once the kneading cycle is complete, leave the dough in the bread machine pan, close the lid, and let it rise right there. Use the machine's "keep warm" or proof function if it has one, or simply leave it in the turned-off machine. Let it rise for 1 to 1.5 hours, or until it has roughly doubled in size.

Line a large baking sheet with parchment paper.

Gently deflate the risen dough by pressing down on it on a work surface.

Using a bench scraper or sharp knife, divide the dough into 8 equal pieces (each about 60-65g).

Work with one piece at a time. Cup your hand over the dough and roll it in small, tight circles on an un-floured part of your counter to create a smooth, taut ball. Repeat with all pieces.

Use a rolling pin to roll each ball into an oval shape, about 15 cm (6 inches) long.

Place the shaped ovals on your prepared baking sheet, leaving at least 3-4 cm (1.5 inches) of space between them to allow for expansion.

Create a warm, humid environment for the buns to rise. The easiest way is to place the baking sheet inside your (turned-off) oven. Place a large, shallow pan of boiling water on the rack below it. Close the oven door.

Let the buns proof for 30-45 minutes, until they are puffy, have filled out the spaces between them, and spring back slowly when you gently poke one with a floured finger.

While the buns are proofing, preheat your oven to 170°C (340°F). Make sure to remove the baking sheet and the pan of water from the oven first.

Remove the proofed dough and brush the surface evenly with beaten egg. Place one hot dog in the centre of each bun.

Pipe a layer of salad dressing, sprinkle with chopped scallions, and finish with a layer of ketchup. Adjust the amount of sauce to taste, avoiding excess to prevent overflow.

Bake on the middle rack at 170°C for 20 minutes, until the buns are golden brown and springy to the touch. If the tops brown too quickly, loosely cover with foil during the last 5 minutes.

Remove from the oven and cool on a wire rack for 5 minutes before serving.