1.
Place eggs in a saucepan, cover with cold water and bring to a boil over medium-high heat. When water boils, remove from heat and cover the saucepan. Let the eggs sit for 16 minutes, then drain and cool eggs in a bowl of ice water. Peel and halve lengthwise.
2.
Pickle the onions by whisking the vinegar, sugar, and 3/4 teaspoon salt together in a mixing bowl. Stir in the onions, cover, and let the onions marinate in the mixture for 1 hour.
3.
Scoop yolks out from split hard-boiled eggs. In a bowl, combine yolks with mayonnaise, pickle juice, mustard, and remaining salt; use a fork to smash the mixture together until smooth.
4.
Pipe or carefully spoon the mashed yolk mixture back into the egg whites. Garnish with pickled onion, and sprinkle with black pepper.