For the burgers: Put the salmon, parsley, basil, onion powder, garlic powder, 1 teaspoon salt, 1/4 teaspoon pepper, the egg and lemon zest in a food processor and blend until evenly mixed and the consistency of ground meat. Form into 4 patties and place on a baking sheet. Refrigerate 20 minutes.
Meanwhile, make the aïoli: Mix the mayonnaise, capers, basil, parsley, garlic and lemon juice in a bowl and refrigerate until serving.
Heat the canola oil in a 12-inch cast-iron skillet over medium heat. Cook the burgers until golden brown and crispy, 3 to 4 minutes per side. Toast and butter the buns. Serve the burgers on the buns with the aïoli, tomatoes and watercress.