Pat the salmon fillets dry and season both sides with salt and black pepper.
Heat 1 tablespoon olive oil in a large heavy skillet over medium-high heat until shimmering.
Add the salmon, presentation side down first if desired, and sear 3–4 minutes per side so the exterior is browned but the center is not fully cooked; remove salmon to a plate.
Reduce heat to medium, add 1 tablespoon butter to the skillet, then add the minced onion and sauté 2–3 minutes until softened and golden.
Add the minced garlic and cook, stirring, about 30 seconds until fragrant.
Pour in 1 cup heavy cream (or half-and-half), stir in 1 tablespoon Italian seasoning and 1/4 cup grated Parmesan, and simmer about 1 minute until the sauce is combined and slightly thickened.
Turn off the heat, return the salmon to the skillet and spoon sauce over the fillets; the residual heat will finish cooking the salmon.
Spoon extra sauce over each serving and serve immediately with pasta or vegetables if desired.
