Preheat oven to 275°F and line a rimmed baking sheet with parchment paper.

Lay salmon fillets on prepared baking sheet and coat evenly with oil. Season with 1/2 teaspoon salt, 1/2 teaspoon pepper and Italian seasoning, and bake for 20-25 minutes, or until the thickest part of the fish begins to flake when pierced with a fork.

While the salmon cooks, make the pesto by combining the pistachios, basil, green onion, rice vinegar and remaining salt and pepper in the bowl of a food processor or blender. Pulse until finely chopped. With the machine running, stream in the water and remaining 1/4 cup olive oil. Transfer pesto to a bowl and fold in grated cheese.