Put unpeeled potatoes and eggs in separate medium saucepans with water to cover. Add 1 tsp. salt to potatoes. Cover pans, bring to a boil over high heat, then reduce heat; simmer eggs for 10 minutes and simmer potatoes until just tender, about 10 minutes. Drain pans, then fill with cold water to cool potatoes and eggs.
Peel eggs and slice crosswise about 1/4 in. thick. Slice potatoes crosswise just a little thicker. Save egg and potato ends for another use and set remaining eggs aside. Set potatoes on a rimmed pan and brush on both sides with oil. Preheat grill to medium (350° to 450°).
Stir mayonnaise, pickle, pickle liquid, onion, mustard, 1 tsp. each chives and dill, 1/4 tsp. pepper, and sugar in a bowl to blend. Chill dressing until used.
Grill potatoes until browned and crisp, turning once with tongs, 7 to 9 minutes. Transfer to a large platter and let cool to room temperature.
Top each potato with about 1/2 tsp. dressing, then an egg slice and a little more dressing. Save any leftover dressing for another use. Sprinkle potatoes with more chopped herbs, then with salt and pepper to taste.
Make ahead: Through step 3, chilled separately, up to 1 day.
Note: Nutritional analysis is per serving.