Preheat the oven to 375°F with a rack in the center position.
In a small bowl, combine the kosher salt, brown sugar, garlic powder, Italian seasoning, and black pepper.
Place the salmon on a rimmed baking sheet, skin side down. Brush the salmon with olive oil, then rub with the spice mixture until completely coated.
Bake for 12 to 15 minutes, or until the fish flakes easily with a fork.
Meanwhile, heat the oil in a large skillet over medium heat. Once the oil is glistening, add the minced garlic and cook, stirring, until fragrant, about 30 seconds.
Stir in the heavy cream, chicken stock, bouillon, ½ cup of the Parmesan cheese, sun-dried tomatoes, Italian seasoning, and ¼ teaspoon red pepper flakes if using. Bring to a simmer and cook, stirring occasionally, until thick enough to coat the back of a spoon. Remove from heat and season with salt to taste.
Discard the salmon skin and nestle the cooked salmon into the sauce. Top with the basil, remaining ¼ cup of Parmesan cheese, and remaining red pepper flakes if using. Serve over cooked pasta or mashed potatoes, if desired.