Preheat an oven. Score the underside of the fish (skin on is ok if that’s what you’ve got) in a small cross-hatch pattern. This is to help the sauce absorb into the fish. Drizzle olive oil into a baking dish, then place the fish on top, scored side down.
Season the fish fillet with kosher salt and freshly ground black pepper. Sprinkle the chopped shallot, chopped parsley, and fresh lemon zest on top. Cover the top of the fish with breadcrumbs.
Pour white wine and dry vermouth around the sides of the pan, then dollop the fish with butter, using your hands to break it up into pieces.
Transfer the cod to the oven and roast until the fish is fully cooked, tender, and flaky. Top with drained capers and a little extra fresh parsley. Enjoy hot with a sprinkle of flaky sea salt and lemon wedges!