Cook potatoes in a large saucepan of boiling salted water for 8 minutes or until tender; drain. Cover to keep warm.
Meanwhile, place salmon, skin-side up, on a chopping board; season with the salt. Turn fish over; cut 5mm (¼-inch) deep slices about 3cm (1¼ inches) apart, cutting crossways along the length of the fish. Combine mint, chives, rind and oil in a small bowl. Rub herb mixture over flesh side of salmon.
Cook asparagus on a heated barbecue (or grill plate), turning, for 3 minutes or until just tender. Remove from heat. Season to taste.
Place salmon, skin-side down, on a heated barbecue (or a large grill plate) for 4 minutes or until the flesh turns paler two-thirds of the way up the side of the salmon. Using two lifters, carefully turn salmon over. Using tongs, carefully remove the skin and place on the barbecue beside the salmon, white-side down. Cook skin and salmon for 2 minutes, or until skin is browned and crisp and salmon is just cooked through. Remove from heat. (To cook the salmon perfectly, keep in mind that it will continue to cook once removed from the heat.)
Place warm potatoes and asparagus in a large bowl with capers, cornichons and three-quarters of the dressing; toss gently to combine. Arrange on a platter, topped with large flakes of salmon. Scatter with extra mint, chives and nasturtium, if using. Top with shards of crisp skin. Serve immediately, drizzled with remaining dressing.
Whisk ingredients in a small bowl to combine. Season to taste.