Preparation

• Soak the skewers in water for at least 30 minutes. Prepare a medium-high (400°F to 475°F) grill fire. Brush clean and oil the grate.
• Put the potatoes in a large pot of cold salted water and bring to a boil; cook until just tender, 5 to 8minutes. Transfer with a slotted spoon to a bowl. Boil the green and wax beans until crisp-tender, about 5 minutes, and drain in a colander.
• Meanwhile, toss the shrimp with 1 Tbs. of the olive oil and 1/4 tsp. each salt and pepper, then thread 4 or 5 on two parallel skewers held about 1/2-inch apart; leave space between the shrimp for even grilling. Refrigerate, covered with plastic wrap, until ready to grill.
• In a small skillet, heat 2 Tbs.of the olive oil with the garlic and anchovies over medium-low heat, mashing the anchovies with a fork until they disintegrate. Continue to cook until the garlic is fragrant but not colored, and the oil starts to shimmer, 3 to 5minutes. Remove from the heat and whisk in the yogurt, 1/4 tsp. salt, and 1/4 tsp. pepper. Season to taste with more salt and pepper.
• Grill the skewered shrimp until just cooked through, 1-1/2 to 2minutes per side. Halve the potatoes lengthwise, and toss with the remaining 1 Tbs. olive oil. Grill the potatoes, cut side down, until grill marks form, about 2 minutes.
• Mound the beans on a platter or divide among 4 dinner plates. Remove the shrimp from the skewers and arrange the shrimp and potatoes around the beans. Whisk the lemon juice into the yogurt dressing, thinning with up to 1 Tbs. water, if needed, to make it easier to drizzle. Drizzle the yogurt dressing over the salads and sprinkle with the parsley. Pass the remaining dressing at the table.