Brown the cod: Melt the butter in a deep frying pan over medium heat. Add the cod fillets and cook for approximately 3 minutes on each side, taking care not to burn the butter. Remove the cod and set aside on a plate.
Cook the shallots and garlic: Add the finely chopped shallots and garlic to the butter remaining in the pan. Cook for 2–3 minutes, until the shallots are soft and translucent.
Deglaze the pan: Pour in the white wine, scraping the bottom of the pan to release any browned residue. Bring to a gentle simmer for about 1 minute.
Reduce the wine: Continue simmering for approximately 4–6 minutes, until the wine has reduced by about half.
Add the cream: Stir in the double cream and simmer gently for 2–3 minutes, until the sauce begins to thicken.
Finish cooking the cod: Return the cod fillets to the pan and spoon the sauce over them. Simmer gently for a further 2–4 minutes, depending on the thickness of the fillets, until the fish is opaque and flakes easily.
Serve: Remove the pan from the heat and serve the cod immediately, spooning the white wine and cream sauce over the fillets.