Brush olive oil over the tops of the salmon filets using a basting brush. Sprinkle the salmon with dried Italian seasoning, kosher salt, and cracked black pepper to ensure each piece is evenly coated.
Heat a large skillet over medium-high heat. Add the seasoned salmon filets to the skillet and sear them for about 3 minutes on each side, or until golden brown and crispy. Once browned, lower the heat and cook until the salmon is cooked through to the center. Transfer the cooked salmon to a plate and set aside.
In the same skillet, add butter and let it melt over medium-high heat. Add freshly minced garlic and sauté for about 30 seconds, just until fragrant. Sprinkle in the flour and stir continuously to form a paste. Gradually whisk in the chicken broth, heavy cream, and parmesan cheese until the sauce is smooth. Stir in the drained sun-dried tomatoes, additional dried Italian seasoning, and lemon zest. Season the sauce with more salt and pepper if desired. Let the sauce simmer for a few minutes to thicken slightly. I like to use freshly grated parmesan here for the richest taste.
Return the cooked salmon filets to the skillet, placing them gently on top of the creamy sauce. Lower the heat to medium-low and let everything simmer together for 10 minutes, allowing the flavors to meld and the salmon to absorb some of the sauce.
Once the salmon is ready, turn off the heat and garnish the dish with fresh basil leaves and a bit more lemon zest if you like extra brightness. Serve warm, ideally over pasta or rice to soak up the delicious sauce.