Step 1: Season the Salmon Pat salmon fillets completely dry with paper towels on all sides. Season both sides generously with salt, black pepper, and red pepper flakes. Add Italian seasoning to the flesh side only. Let rest at room temperature for 10 to 15 minutes before cooking.
Step 2: Sear the Salmon. Heat a large skillet over medium-high heat for 2 minutes. Add sun-dried tomato oil. When oil shimmers, place salmon skin side down. Do not move them. Cook 3 to 4 minutes until skin is golden and crisp and releases naturally. Flip and cook the flesh side for 2 minutes. Remove to a plate.
Step 3: Make the Sauce Base. Reduce the heat to medium. Add butter to the same pan. Once melted, add minced garlic. Cook exactly 30 seconds, stirring constantly. Add drained sun-dried tomatoes and stir 30 seconds to warm through.
Step 4: Build The Sauce. Add chicken broth. Scrape every bit of fond from the pan bottom. Allow broth to reduce by half over approximately 2 minutes. Reduce the heat to medium-low. Add heavy cream. Stir gently and simmer 3 to 4 minutes until the sauce begins to thicken. Add freshly grated parmesan in three separate additions, stirring between each. Season with salt and pepper after tasting.
Step 5: Finish the Salmon Return salmon to the pan. Nestle into the sauce. Spoon sauce over each fillet. Reduce the heat to low. Cover and cook 3 to 4 minutes until salmon reaches 130 to 135°F (54 to 57°C).
Step 6: Rest and Serve. Remove pan from heat. Add fresh basil and lemon zest off the heat. Rest 2 minutes. Serve immediately over pasta, rice, or with crusty bread.