Step 1

Place a fine mesh strainer over a large bowl and line with cheesecloth. Place yogurt in cheesecloth; let stand at room temperature until thickened and about 1/4 cup liquid has strained through cheesecloth into bowl, about 30 minutes.

Step 2

Meanwhile, preheat oven to 425°F. Toss together potatoes, 1 1/2 tablespoons of the oil, 1/2 teaspoon of the salt, and 1/4 teaspoon of the pepper in a large bowl. Arrange potatoes, cut side down, along outer edges of a large rimmed baking sheet lined with aluminum foil. Roast in preheated oven until potatoes are golden brown in spots on bottom, about 25 minutes.

Step 3

While potatoes roast, remove salmon from refrigerator, and let stand at room temperature. Smash garlic cloves on a cutting board, and roughly chop. Sprinkle with 1/4 teaspoon of the salt. Using flat side of a large knife, drag knife back and forth over garlic to form a paste. Transfer garlic paste to a small bowl. Add olives, 3 tablespoons of the butter, and 2 tablespoons of the parsley; mash using a spoon until combined. Spread butter mixture evenly over salmon fillets.

Step 4

Remove baking sheet from oven. Rotate potatoes, without flipping, on baking sheet 90 or 180 degrees. Arrange salmon fillets, skin side down, in center of baking sheet, evenly spaced apart. Return baking sheet to oven, and roast at 425°F until salmon is just opaque in center, about 10 minutes.

Step 5

While salmon roasts, stir together strained yogurt, capers, honey, lemon zest, 1 tablespoon of the parsley, and remaining 1 1/2 teaspoons oil and 1/4 teaspoon pepper in a small bowl. Set aside until ready to serve.

Step 6

Microwave green beans and water in a large microwavable bowl on HIGH until tender-crisp, about 2 minutes. Drain. Add remaining 1/4 teaspoon salt and 1 tablespoon butter; toss to coat.

Step 7

Spread 3 tablespoons yogurt mixture along 1 side of each of 4 plates. Arrange potatoes evenly on top of yogurt mixture, and place salmon alongside potatoes. Arrange green beans alongside, and sprinkle evenly with remaining 1 tablespoon parsley.