For the salmon: Preheat the broiler to high and set an oven rack on the top third of the oven if your broiler is on top.
Place the salmon on a rimmed baking sheet. Sprinkle the pieces evenly with the salt and drizzle both sides with the olive oil. Broil until the fish flakes easily but is still moist inside, 4 to 5 minutes depending on the thickness of the salmon. Remove to cool slightly, about 3 minutes.
For the salad: Meanwhile, soak the fennel rings and radish matchsticks in a bowl of ice water for 15 minutes. Drain well and spin or pat dry. Whisk together the olive oil, apple cider vinegar, Dijon and salt in a medium bowl. Add the fennel, radish and basil to the dressing and toss well to coat.
Place a small mound of salad in the center of each of 4 plates. Top with a piece of salmon and a pinch more salad.