Slice potatoes in half and season with salt and pepper.
In a small bowl, combine the red onions with sherry vinegar and salt. Chill while you make everything else (or make ahead, the longer they sit the better).
Whisk together the dressing ingredients at the bottom of a large bowl. Set aside.
Heat a grill pan* to high heat and brush with oil. Place the potatoes, cut side down and let them cook without moving them until nice char marks start to form (flip one to check).
Flip them, add a good squeeze of lemon juice and continue cooking until roasted on the outside and tender in the middle. Reduce heat and cover if necessary (my grill pan doesn't have a cover, but we placed a baking sheet over it). I cooked my 1" potatoes for about 20-25 minutes total.
Transfer cooked potatoes to the large bowl with the dressing and toss to coat. Let cool and toss with arugula, onions, capers, chives and lemon zest.
Taste and add more dressing to your liking. Serve at room temp, or make ahead and chill.
*if using an outdoor grill, you may need a pan or grill basket so the potatoes don't fall through the grates. You could also could boil your potatoes or roast them in the oven.
Recipe by Love and Lemons at https://www.loveandlemons.com/grilled-potato-arugula-salad/