Combine the shallot, ½ teaspoon salt, and ½ cup water in a small bowl. Let sit until softened slightly, 12 to 15 minutes; drain.
Meanwhile, steam the broccolini in ½ inch of water until tender, 4 to 6 minutes; drain. Toss with the capers, shallot, 1 tablespoon of the oil, and ¼ teaspoon pepper in a medium bowl.
Season the salmon with the coriander, ¼ teaspoon salt, and ½ teaspoon pepper. Heat the remaining tablespoon of oil in a large nonstick skillet over medium-high heat. Add the salmon and cook until opaque throughout, 2 to 3 minutes per side.
Serve the salmon and broccolini with lemon wedges.