On a cutting board, place one slice of cheddar cheese, place the slice of ham on top of the cheddar. If the ham is not square, trim it to the same size as the slice of cheese. Scramble your leftover ham trimmings with onion, peppers, and eggs. Cut the ham and cheese into 4 equal squares. Repeat with the rest of the ham and cheese.
Stack the ham and cheese until you have 10 layers of ham and 10 layers of cheese.
On a cutting board, peel the potatoes. Shred the potatoes into a large bowl lines with a thin towel.
Once all of your potatoes are shredded, wrap the towel tightly and twist to squeeze out all of the water from the potatoes. Discard the potato water.
Place the shredded potatoes into a clean bowl, add 1 teaspoon of salt, pepper, flour, and egg. Mix thoroughly.
Wrap the potato mixture around the ham and cheese cube. Flatten each side to create a cube. Repeat with the rest of the cubes.
On a parchment paper-lined baking sheet place the hash brown cubes. Freeze for 2-3 hours or until solid.
Heat 4 inches (10 cm) of oil in a large pot until the temperature reaches 350˚F (180˚C).
Fry each cube for 4 minutes until golden brown. Place on a cooling rack or drain on paper towel. Let cool for 5 minutes. Sprinkle with the rest of the salt.