Preheat the oven to 450°. In a large saucepan, cover the eggs with water, add the vinegar and bring to a rapid boil. Cover the saucepan and remove it from the heat; let stand for 15 minutes. Drain the eggs and cool them under cold running water, shaking the pan vigorously to crack the shells. Let the eggs cool in the water.
Meanwhile, quarter the bread slices on the diagonal and arrange them in a single layer on a large cookie sheet. Toast the bread in the oven for about 6 minutes, turning once, until barely browned.
Shell the eggs and halve them lengthwise. Coarsely chop half of the egg whites and transfer them to a large bowl. Add the remaining whites and all of the yolks to a food processor along with the mayonnaise and mustard and process until smooth. Scrape the mixture into the bowl and blend with the chopped egg whites. Season with salt and pepper.
Top the toast points with the egg spread and dust lightly with paprika. Arrange the toasts on a platter and serve. Alternatively, serve the egg spread in a bowl with the toast points alongside.