How to Make It
Heat a large cast-iron grill pan. In a medium bowl, toss the potatoes with 2 tablespoons of the olive oil and season with salt and pepper. Grill over moderate heat, turning, until golden and tender, about 20 minutes. Transfer to a work surface and let cool slightly, then coarsely chop and transfer to a large bowl.
In a large bowl, toss the shrimp with 2 tablespoons of the oil and season with salt and pepper. Grill over moderately high heat, turning once, until golden and just cooked through, about 4 minutes. Transfer to a plate and drizzle with 1 tablespoon of the lemon juice.
In a small bowl, whisk the remaining 3/4 cup of olive oil with the dill and chives and season with salt and pepper.
Add 1/3 cup of the herb oil to the potatoes along with the arugula, preserved lemon peel and the remaining 1 tablespoon of lemon juice. Season with salt and pepper and toss to coat. Spoon the potato salad onto plates and top with the shrimp. Serve the remaining herb oil on the side.