Heat olive oil in a large nonstick skillet set over medium heat.
Season salmon fillets with salt and pepper.
Add salmon to the heated oil and cook for 6 to 8 minutes, or until cooked 3/4-of the way UP. 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. To check for doneness, you can use an instant read meat thermometer; salmon is done when the thickest part of the salmon registers at 145˚F.
Remove salmon from skillet and set aside.
In the same skillet add 1 tablespoon of the reserved sun-dried tomatoes oil and heat it over medium heat.
Add onions and cook for a minute. Add the remaining tablespoon of sun-dried tomatoes oil only if needed.
Stir in garlic, sun-dried tomatoes, and Italian seasoning; cook for 1 minute, or until fragrant.
Add vegetable broth to the skillet and bring to a simmer.
Stir in the heavy cream. Cook until heated through. Taste for salt and pepper and adjust accordingly.
Add salmon back to the skillet and cook for 2 more minutes, or until the sauce is a bit thickened.
Remove skillet from heat; let stand couple minutes. Note that the sauce will continue to thicken as it cools.
Spoon sauce over the salmon fillets.
Garnish with parsley and serve.