Peel the potato and cut it into large chunks. Place in a pot/pan and cover with cold water. Place on a medium heat and bring to a boil.
Once boiling, reduce heat so the water simmers and cook until the potato is tender to a knifepoint. The timing will depend on the size of the pieces but it will take roughly 10 minutes after boiling, so check regularly a little before then. One tender, remove from the heat and drain - you don't want to overcook.
Return the potatoes to the warm pot, uncovered and let the warmth help them steam and dry a little. Either place through a ricer or mash in a wide bowl/dish while they are still warm to help them lose a bit more steam. Allow to cool (some prefer to cook a day ahead, but at least not hot is best).
Add the egg yolk, flour, butter and salt to the mashed potatoes, bring everything together and mix, but take care not to overmix. If the mixture is too sticky, add a little extra flour, but you don't want overly firm, and remember you will be rolling in flour.
Lightly flour a clean work surface and take a small handful of the dough. Roll it out into a log, roughly 1 inch (2.5cm) diameter or slightly thinner. Cut the log into 1 inch (2.5cm) slices. Roll each piece with floured hands into finger shapes with pointed/tapered ends so they are slightly pointed on either side. Alternatively, you can just take a spoonful of the mixture, roll it then flatten to give the same finger with tapered end shape.
Repeat with the rest of the dough and set the formed noodles aside on a floured board/baking sheet. I recommend forming all of the noodles before cooking.
Bring a wide pot of water to a roaring boil (you want a good 2inches/5cm or more depth). Carefully add some of the noodles to the water, taking care not to overcrowd the pot. Once they rise to the surface, remove them with a slotted spoon and transfer to a plate/baking dish. Try to make sure they don't overlap or get too crowded. Repeat with additional batches.