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1
Make the salad: Place the potatoes, carrot and turnip in a medium-size saucepan. Add water to cover by 2 inches, bring to a boil over medium-high heat, then reduce the heat to medium-low and simmer, partially covered, until all the vegetables feel tender when pierced with a skewer, about 15 minutes for the carrot and turnip, a bit longer for the potatoes.
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2
As the vegetables become soft, use a slotted spoon to transfer them to a bowl. Take care not to over cook.
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3
Bring the water back to a boil, add the green beans, and cook until tender, about 5 minutes (they should be neither al dente or overcooked). Drain the beans, blot them dry with paper towels and set aside. Let the vegetables cool to room temperature.
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4
Peel the potatoes, carrot and turnip, then cut them into small dice and transfer to a mixing bowl.
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5
Cut the green beans into a 3/4-inch lengths and add them to the bowl with the diced vegetables. Then add the peas, tuna, roasted peppers and the 2 chopped eggs. Using a sturdy fork, mash the salad until it has a chunky-creamy consistency.
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6
Make the dressing: Place the olives, anchovies, 2 tablespoons of the mayonnaise, and 3 tablespoons water in a blender and process until a medium-fine paste forms. Stir the olive mixture into the the salad.
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7
Place the remaining maynnaise and the lemon juice into a small bowl and whisk to mix, then stir into the salad. Season with salt and pepper to taste. If you'd like the salad to be moister, add more mayo.
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8
Cover the bowl with plastic wrap and let the salad stand for about 2 hours. (You can make the salad up to 1 day ahead. Refrigerate it and let it come to room temperature before serving). To serve, spoon the salad on a shallow serving dish and garnish with the grated egg.