Prepare the Potato Dough

1. In a large mixing bowl, combine mashed potatoes, 2/3 cup of bread flour, and instant yeast. Stir until well combined.
2. Incorporate the egg and a pinch of salt into the mixture. Adjust salt according to preference.
3. Gradually add the remaining bread flour, blending until a soft and slightly sticky dough forms. Add more flour if needed, depending on the mashed potatoes’ moisture content.

Kneading and Rolling

1. Lightly dust a clean countertop with bread flour.
2. Transfer the dough to the floured surface and knead briefly until smooth.
3. Roll out the dough to about 1/4 inch (0.6 cm) thickness.

Cutting the Discs

1. Using a round cookie cutter or the rim of a cup (about 2.5 inches or 6.35 cm in diameter), cut out approximately 24 discs from the rolled dough. Re-roll any scraps and continue cutting until all dough is used.

Prepare the Ham and Cheese

1. For each cheese slice, wrap it with a slice of ham, ensuring the cheese is completely enveloped.

Assembling the Potato Cakes

1. Lay out half of the potato dough discs on your work surface.
2. Place the ham-wrapped cheese slices onto the center of each disc.
3. Top each with another potato dough disc, pressing the edges together firmly to seal and ensure the filling is well-enclosed.

Coating

1. Dip each stuffed potato cake into bread crumbs, ensuring they are evenly coated on both sides.

Frying

1. In a large skillet or frying pan, pour in oil to a depth suitable for shallow frying.
2. Heat the oil over medium heat. To test, dip a wooden spoon or small piece of dough into the oil; it’s ready when small bubbles form and it gradually turns golden.
3. Carefully place a few potato cakes into the hot oil. Fry until deep golden brown on one side, flip, and fry the other side.
4. Once done, remove the potato cakes and place them on paper towels to drain excess oil.

Serving

1. Serve the Ham and Cheese Stuffed Potato Cakes while hot.