Preheat an oven to 200°c/180°c fan (390°f/350°f).Place your potato onto a baking tray, drizzle with the vegetable oil then bake in the preheated oven until the skin is crispy & the inside is soft*. This will take 1-1.5 hours.Use a sharp knife to check that the potato is cooked all the way through.Once the potato is cooked, you can turn your oven off & preheat it again, later on. Let the potato cool slightly then cut in half & scoop out the flesh. Use a potato ricer (or fork) to mash the potato then weigh out 90g. Chop the crispy potato skin into small pieces then add into the mash potato. Leave to cool to room temperature.
Next, place the milk & water into a jug & warm in the microwave to 38°c/100°f (alternatively you could heat this up in a saucepan then transfer to a jug), then whisk in the yeast & leave to go bubbly, 5-10 minutes.
Add the flour, mash potato (and skin), salt, sugar, milk powder & egg into the bowl of a stand mixer. Give the activated yeast a whisk then add to the bowl. Using the dough hook, knead the dough on a medium speed until smooth & starting to come away from the sides of the bowl, around 5 minutes. With the mixer still going, add in the butter a small amount at a time, incorporating each piece fully before adding more. Once all the butter has been incorporated, keep mixing until the dough passes the window pane test, 5-10 minutes.
Transfer the dough to a lightly oiled bowl, cover with clingfilm or a tea towel & leave to double in size at room temperature, 45 minutes - 1 hour.
Once risen, knock the dough back then transfer to a lightly floured work surface. Using a bench scraper, divide the dough into 5 equal pieces, they should weigh around 110g each.
To shape, take a piece of dough & bring the edges into the middle. Flip the dough over & use cupped hands to shape into a tight ball. Dragging the seam on the work surface helps increase surface tension.Transfer to a lined baking tray & repeat with the remaining dough. Once shaped, cover with another baking tray (flipped upside down) or loosely with oiled clingfilm & leave to double in size at room temperature, 30 - 45 minutes.
In the meantime, turn your oven back on & preheat to 180°c/160°c fan (350°f/320°f).
Combine the egg & water with a pinch of table salt then brush the buns generously with the egg wash.
Sprinkle the top of each bun with sesame seeds then bake in the preheated oven for 15-20 minutes or until a deep, golden brown.
Once baked, brush each bun with melted butter then leave to cool completely.