Peel the eggs, then slice in half lengthwise and remove the yolks from the whites. Place the yolks in a medium bowl and add mayonnaise, mustard, vinegar, and salt. Mash with a fork until smooth.

Transfer to a large ziploc bag and snip off about 1/2-inch of one corner to pipe the deviled egg filling into the center of 12 of the egg white halves. Chop and reserve the remaining egg white halves and any unused deviled egg filling (usually around 1/4 cup) for adding to the potato salad.

Scrub the potatoes well, then dice into 1/2-inch pieces and add to a large pot. Fill with cold water until it covers the potatoes by 1 inch. Add 1 tablespoon of salt to the water and bring to a boil over high heat, then reduce heat to medium-high. Cook just until the potatoes can be pierced easily with a fork, then drain well and transfer to a large mixing bowl. Add the vinegar and stir. Let sit 15 minutes to cool slightly.

Transfer potato salad to a large serving bowl, then arrange the deviled eggs on top. Sprinkle with paprika and chill for at least 1 hour or overnight before serving.