Place cut potatoes in a large pot. Cover with one inch of cold water.
Bring to a boil over high heat, then reduce heat to medium to maintain a gentle boil. Cook for 7 to 10 minutes, stirring occasionally, until fork-tender. Be careful not to overcook, since they can get mushy. Check for doneness early in the process. A fork should be able to glide through them easily without them falling apart.
If you have a spider spoon/skimmer, use it to gently transfer them out of the pot and into a large mixing bowl. Otherwise, drain them in a colander. Let them cool slightly while you prep the other ingredients.
Combine the slightly cooled, cooked potatoes, dill pickles, dill, and green onions in a large mixing bowl. Stir gently to combine.
In a separate bowl or measuring cup, whisk together the olive oil, dill pickle juice, white wine vinegar, Dijon, salt, and pepper until creamy and emulsified.
Pour the dressing over the salad, and gently stir until all of the ingredients are coated. Taste and adjust the seasonings as desired.
You can enjoy this salad while the potatoes are still warm if desired. For a more intense flavor, let it chill in the fridge for at least one and up to a few hours. Give it a drizzle of olive oil or a dash of brine or white wine vinegar just before serving.
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