Pat the 4 salmon filets dry with paper towels. Brush both sides of each filet with the 1 tablespoon olive oil. Season evenly with 2 teaspoons dried Italian seasoning, ½ teaspoon Kosher salt, and ¼ teaspoon cracked black pepper.
Heat a large skillet over medium-high heat (no additional oil). When the skillet is hot, add the salmon filets in a single layer. Cook until golden brown and crispy, about 3 minutes per side. Reduce the heat if the exterior is browning too quickly; cook until the salmon is just cooked through (depending on thickness, an additional 1–3 minutes may be needed). Transfer the salmon to a plate and set aside.
Return the same skillet to medium heat and add 3 tablespoons butter. Melt the butter.
Add 2 teaspoons minced garlic to the melted butter and sauté about 30 seconds, stirring, until fragrant (do not let the garlic brown).
Sprinkle in 3 tablespoons flour and stir constantly to form a smooth paste (a roux). Cook the roux about 1 minute, stirring, to eliminate the raw flour taste.
Gradually whisk in 1 ½ cups chicken broth until smooth, then whisk in ¾ cup heavy cream. Bring the mixture to a gentle simmer while stirring to combine.
Stir in ½ cup grated Parmesan until melted and incorporated into the sauce.
Add the drained ½ cup sun-dried tomatoes, 1 teaspoon dried Italian seasoning, and 1 teaspoon lemon zest. Taste the sauce and season with additional salt and cracked black pepper if needed.
Simmer the sauce for 3–5 minutes, stirring occasionally, until it thickens to a sauce that coats the back of a spoon.
Return the salmon filets to the skillet, nestling them into the sauce and spooning sauce over the tops so they are coated.
Reduce the heat to medium-low and simmer gently for 3–5 minutes more to reheat and finish cooking the salmon through.
Garnish with fresh basil leaves and additional lemon zest if desired. Serve warm.