
Season the cod. Preheat the oven to 400°F (200°C). Place the cod in a baking dish and drizzle with oil, coating both sides of the fish. Season both sides with salt and pepper.
Bake the cod. Bake in the oven for 14 to 15 minutes, or until the cod is opaque and flakes easily with a fork.
Make the sauce. Meanwhile, while the cod is baking, melt 1 tablespoon of butter in a pan over medium heat. Add the shallots, whisk for 30 seconds, then add the wine, vinegar, and orange juice, and continue whisking until the liquid is almost completely reduced (about 2 tablespoons of liquid remaining).
Finish the sauce. Add the cream and salt and bring to a boil. Turn the heat down to medium low, add the orange zest and remaining butter a few pieces at a time, while whisking rapidly and continuously.
Serve. Plate the baked cod and drizzle the citrus buerre blanc sauce on top before serving.