Pat the salmon fillets dry and season both sides with salt and black pepper.
Make the basil sauce by blending basil, garlic, lemon juice, olive oil, water, and Parmesan cheese, if using, until smooth. Taste and adjust seasoning.
Heat 2 tablespoons olive oil in a large skillet over medium-high heat.
Place the salmon in the skillet skin-side down if applicable, and cook for 4 to 5 minutes.
Flip the salmon and cook for another 3 to 4 minutes, or until cooked through and flaky.
Transfer the salmon to plates and spoon the basil sauce over the top before serving.