To a medium pot, bring water to a boil, and add the salt. Slide the potato chunks into the water and let it cook for 15 mins.
Drain and mash the potatoes with a fork or push the potatoes through a metal strainer to make them extra smooth. Add butter and mix until well incorporated.
Dip a sheet of rice paper into a bowl of room-temp water for 10 seconds. Place the wet rice paper sheet onto a clean, dry surface.
Place a small piece of the cheese slice into the centre of the rice paper.
Scoop up 1/4 cup of mashed potatoes, layering it on top of the cheese. Mould the mashed potato into a flat rectangular shape.
Bring the bottom portion of the rice paper up, top portion down, right to left, left to right, until you have a tightly wrapped rice paper potato dumpling.
Repeat steps 3 and 6, two more times until you have a total of 3 layers of rice paper wrapped around the mashed potatoes.
To a non-stick pan on medium-high heat, add in enough oil to coat the bottom of the pan.
Once the oil is heated up, slide the dumplings in, and let each dumpling cook for 30 seconds on each side.
Transfer to a wire rack to cool (Note 1).
Serve immediately with a side of warm gravy for dipping.