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put the potatoes in a large pot and add enough cold water to cover them by 1 inch. add a pinch of salt. bring to a boil and cook until the potatoes are tender but not mushy, about 15 minutes. drain. set aside until cool enough to handle.
while the potatoes are still warm, cut them into quarters and place them in a large bowl. add the scallion, relish, mayonnaise, and eggs. toss until well combined. taste and season with salt and pepper.
cover and chill until ready to serve, at least 1 hour or up to overnight.