Pat the salmon fillets dry with paper towels. Season generously on both sides with salt, black pepper, and a pinch of Italian seasoning.
Heat the olive oil in a large skillet over medium-high heat. Once the oil is shimmering, place the salmon fillets skin-side down (if using skin). Sear for 4-5 minutes until the skin is crispy and golden. Flip and cook for another 2-3 minutes. The salmon should be just cooked through and flaky. Transfer the salmon to a plate and set aside.
Reduce the heat to medium. Add the 3 tablespoons of butter to the same skillet. Once melted, toss in the minced garlic and chopped sun-dried tomatoes. Stir constantly for about 1 minute until the garlic is fragrant and the tomatoes soften slightly. Do not let the garlic burn.
Pour in the heavy cream and chicken broth, stirring to combine. Bring the mixture to a gentle simmer. Sprinkle in the remaining Italian seasoning and stir. Let it cook for 2-3 minutes, allowing the sauce to thicken and blend with the Parmesan.