Preheat the oven to 375°F (190°C) and position the rack in the top third; line a baking sheet with foil.
Place the salmon on the prepared sheet and rub or brush with about 1 teaspoon olive oil; season with salt and pepper.
Bake the salmon until just cooked through, about 10–15 minutes depending on thickness; internal doneness is when the flesh flakes easily with a fork.
While the salmon bakes, make the zesty mayo: in a small bowl combine 1/4 cup mayonnaise, 1 teaspoon lemon juice, zest of 1/2 lemon, and 1 teaspoon finely chopped fresh parsley; whisk until smooth and set aside.
If you like toasted bread, spread a little butter on the cut sides and toast in a skillet over medium-high heat until golden.
Assemble the sandwiches: spread zesty mayo on the bread, top with a layer of arugula, then flake or place the baked salmon on top and close the sandwich; serve immediately.