Pat both sides of the salmon fillets completely dry with paper towels. Season all over with the kosher salt and black pepper.

Heat the olive oil in the skillet over medium-high heat until it shimmers. Place the fillets skin-side down and cook undisturbed for 4 to 5 minutes, until the edges turn opaque and the skin is crisp. Flip and cook 2 to 3 minutes more, then move the salmon to a plate. It does not need to be cooked through yet.

Reduce the heat to medium and melt the butter in the same pan. Add the garlic and stir for 30 to 60 seconds, until fragrant but not browned. Pour in the heavy cream and bring it to a gentle simmer. Stir in the Parmesan, Italian seasoning, and red pepper flakes if using. Simmer 2 minutes, stirring, until the sauce lightly coats the back of a spoon.

Add the spinach a handful at a time, stirring after each addition, until it has wilted into the sauce, about 1 to 2 minutes. Stir in the lemon juice if using.

Nestle the salmon back into the sauce, skin-side up if it has skin. Spoon the sauce over the fillets and simmer gently for 3 to 4 minutes, until the thickest part reaches 145°F (63°C) and flakes easily with a fork. Garnish with parsley and serve with lemon wedges.