Heat the olive oil in a large nonstick skillet set over medium heat.

Season the salmon fillets with salt and pepper. Add the fillets to the heated oil and cook for 6 to 8 minutes, or until cooked 3/4 of the way up. The cooking time will depend on the thickness of the fillet. Using a fish spatula, carefully flip over the salmon and cook for 3 to 4 more minutes, or until cooked through. Remove the fillets from the skillet and set aside.

In the same skillet, add 1 tablespoon of the reserved sun-dried tomato oil and heat it over medium heat. Add the onions and cook for a minute. Add the remaining tablespoon of sun-dried tomato oil only if needed.

Stir in the garlic, sun-dried tomatoes, and Italian seasoning; cook for 1 minute, or until fragrant.

Add the vegetable broth to the skillet and bring to a simmer. Stir in the heavy cream and cook until heated through. Taste the sauce for salt and pepper and adjust accordingly.

Return the salmon fillets to the skillet and cook for 2 more minutes, or until the sauce is slightly thickened.

Remove the skillet from the heat and let it rest for a few minutes. The sauce will continue to thicken as it cools. Then, spoon the sauce over the salmon fillets, garnish with parsley, and serve.