Creamy mayonnaise, a few good seasonings and crisp veggies make this irresistible - plan on making plenty! The secret to the wonderful flavor is mixing the scallions and a boiled egg into the dressing - tantalizingly good!
Whisk all the dressing ingredients together in a small bowl.
Put the potatoes and 2 Tbs. salt in a 6-quart pot and add enough cold water to cover by 1 inch. Bring to a boil over high heat and reduce the heat to maintain a simmer. Cook the potatoes until barely tender when poked with a fork or skewer, 20 to 25 minutes. If the potatoes aren't all the same size, remove them as they are cooked. (Baby potatoes will take 5 to 10 minutes.)
Gently drain the potatoes in a colander and set aside until just cool enough to handle. Using a paring knife, peel the potatoes by scraping off the skin. (Skip this step if using baby potatoes.) Cut the potatoes into 3/4-inch chunks. With your fingers, pull apart any pieces that are stuck together.
When the potatoes have completely cooled, gently fold the cucumbers, radishes, scallions, hard-boiled eggs, basil, and parsley into the potatoes. Fold in enough dressing to generously coat the potatoes (you may not need all of the dressing). Season to taste with salt and pepper. Sprinkle lightly with dried parsley flakes and a bit more paprika. Serve cold.
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