Pat the cod dry and season: Use paper towels to dry the fillets well. Season both sides with salt, black pepper, and a light sprinkle of Italian seasoning. Dry fish sears better and stays flaky.
Sear the fish: Heat a large skillet over medium-high.
Add olive oil and 1 tablespoon butter. When hot and shimmering, add the cod. Sear 2–3 minutes per side until lightly golden.
Transfer to a plate; the fish will finish cooking in the sauce.
Sauté aromatics: Lower heat to medium. Add remaining butter. Stir in shallot and cook 1–2 minutes until translucent.
Add garlic and cook 30 seconds until fragrant. Avoid browning the garlic.
Add tomatoes and deglaze: Stir in sun-dried tomatoes (and cherry tomatoes, if using). Cook 1 minute.
Pour in broth and scrape up any browned bits; let it simmer for 2 minutes to reduce slightly.
Build the cream sauce: Stir in heavy cream, Parmesan, Italian seasoning, and a small pinch of red pepper flakes. Simmer gently for 2–3 minutes, stirring, until slightly thickened.
Wilt the greens: Add spinach and toss until just wilted. Taste the sauce and adjust salt and pepper.
Add a little more broth if it gets too thick.
Finish the fish: Nestle the cod back into the skillet with any juices. Spoon sauce over the fillets. Simmer on low for 3–5 minutes, until the cod flakes easily and reaches an internal temp of about 145°F.
Brighten it up: Add lemon zest and juice to taste.
Start with 1 tablespoon and add more if you want extra brightness.
Garnish and serve: Sprinkle with chopped basil or parsley. Serve straight from the skillet with crusty bread, pasta, rice, or mashed potatoes to catch the sauce.