Heat 1 teaspoon of the oil in a large nonstick skillet over medium heat. Season the salmon with ¼ teaspoon each salt and pepper.
Cook the salmon until opaque throughout, 4 to 6 minutes per side. Transfer to a plate and refrigerate until cool, about 15 minutes.
Meanwhile, in a large bowl, combine the bulgur with 2 cups boiling water. Let stand until tender, about 25 minutes. Drain and return it to the bowl.
Toss the bulgur with the cucumbers, parsley, mint, onion, lemon juice, remaining tablespoon of oil, ½ teaspoon salt, and ¼ teaspoon pepper.
Using a fork, flake the salmon into large pieces. Gently fold it into the bulgur mixture.
