Working with one egg at a time, dredge each peeled, dry, soft-boiled egg through the flour, the egg mixture, and the breadcrumbs.
Carefully set the coated egg in the batter, spooning batter over the top. (Don't roll the egg in the batter; the breadcrumbs will fall off.)
Scoop up the coated egg with a spoon to transfer it to the hot oil. Use a second spoon to push the egg into the oil. Cook for 1 minute, or until golden brown. Transfer the egg to a paper towel-lined plate.
Repeat this process for all the eggs. (Each time you cook an egg in the oil, the temperature of the oil may drop, so make sure it is at 350°F.)
Serve immediately with hot sauce and ranch or blue cheese dressing.