Place whole eggs in the bottom of a pot, and fill the pot with water until the eggs are submerged. Cover the pot and bring it to a boil on your stovetop. Once the pot is boiling, remove the lid, and let the eggs boil for 12 minutes until they are hard-boiled. After 12 minutes, transfer the eggs to an ice bath until they’re cooled. Once the eggs are cooled, peel them and place them in a clean mixing bowl. The eggs don’t need to be peeled perfectly, since you’ll be mashing them next.
Mash the hard-boiled eggs in the mixing bowl until they have minimal chunks of visible egg white. You can use a potato masher or a fork to achieve this. Then, add mayonnaise, salt, pepper, garlic powder, and shredded cheese to the eggs, and continue mashing them until you have an even mixture with a paste-like consistency. There may be very small pieces of egg whites visible, but the mixture should be mostly lump-free.
Place a large cast-iron or non-stick skillet over your stovetop and begin heating the avocado oil in it over medium-high heat. A cast-iron skillet is preferred for this recipe, but you can use a non-stick skillet as well if it is in good condition. If you have to cook the egg fritters in batches due to the size of your skillet, start with an appropriately portioned amount of the avocado oil. While the oil is heating, portion the egg fritters into 4-tablespoon portions. If you own a #40 scoop, each portion is two scoops.
Pack your first portion of egg fritter into a dense ball. Then, place the ball in the skillet of hot oil, and use a spatula to press the ball down into a patty. At first, the patty will look a little more like a crab cake at about ¾”-thick, but it will spread during the cooking process. Repeat until your skillet is filled with egg fritter patties. Let the fritters cook on one side until you start to smell the egg browning in the pan. Then, reduce the heat to a medium temperature.
Continue cooking the fritters on the same side. You may need to utilize a splatter screen to keep safe from the hot oil. Don’t flip the fritters until they naturally release from the skillet using your spatula. Gently flip the fritters over and continue cooking until they fry on the other side. Once they’re done, gently transfer the egg fritters to a serving plate. You can use a paper towel to soak up any excess frying oil that has pooled up.