Special equipment: a pastry bag fitted with a small round pastry tip
Preheat the oven to 350 degrees F. Coat an 8-inch square baking dish with cooking spray.
Separate the egg whites and yolks into 2 small bowls; set aside the yolks. Whisk the whites until just foamy, transfer them to the prepared baking dish, cover the dish with foil and bake until the whites have fully set, about 20 minutes. Let cool completely in the baking dish.
While the whites are baking, beat the yolks until smooth. Lightly coat a medium nonstick skillet with cooking spray. Add the yolks, and scramble over medium low until fully cooked and slightly dry, 4 to 5 minutes.
Transfer the yolks to a food processor. Add the mayonnaise, vinegar, mustard, 1/4 teaspoon salt and a few grinds of pepper, and pulse until smooth and creamy. Transfer the yolk mixture to a pastry bag fitted with a small round tip.
Turn the egg whites out of the baking dish onto a cutting board. Cut into even 1-inch squares. Pipe swirly dollops of the egg yolk onto each square. Sprinkle each with paprika and chives if using.
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