Place potatoes in a medium pot; cover with 2 inches water.
Season water generously with salt. Bring to a boil, then
reduce heat and simmer until potatoes are knife-tender,
about 25 minutes for russets, 15 for small reds or
fingerlings. Drain. When just cool enough to handle, chop
potatoes into 1-inch pieces (peel if using russets).
Drizzle with 1 to 2 tablespoons vinegar; let cool.
Combine egg, mayonnaise, dry mustard, and celery seeds in
a large bowl; season with salt and pepper, and whisk to
Stir in potatoes, celery, onion, cornichons, scallion, and
parsley. Refrigerate at least 30 minutes or up to 1 day
before serving, topped with sliced hard-cooked eggs and
sprinkled with sweet paprika, if desired.
2 pounds russet, small red, or fingerling potatoes