Wrap shredded potatoes in cheesecloth and wring out until dry, approximately 2 minutes.
Place in a large bowl and add one egg, salt, pepper, garlic and onion.
Heat a nonstick skillet on medium-high heat and add oil.
Place 1/2 cup of the shredded potato mixture in an even layer and cook for approximately 2 minutes until golden. Flip and use a 2-inch round cookie cutter to remove the center of the patty.
Drop a single egg in the patty and cook until whites are set.
Remove patty from pan and repeat until all potatoes are used. Top with chives and large flake salt.