Preheat and prep: Heat the oven to 425°F (220°C). Line a large sheet pan with parchment for easy cleanup.
Pat the cod dry with paper towels and set aside.
Toss the veggies: In a large bowl, combine potatoes, bell pepper, red onion, and broccoli. Drizzle with 2 tablespoons olive oil. Add 1/2 teaspoon salt, 1/4 teaspoon pepper, paprika, and oregano.
Toss to coat well.
Start the roast: Spread the veggies in a single layer on the sheet pan. Roast for 12 minutes to give the potatoes a head start.
Make the lemon-garlic mix: In a small bowl, stir together the minced garlic, lemon zest, 2 tablespoons lemon juice, remaining 1 tablespoon olive oil, butter (melted), Dijon, and honey if using. Season with a pinch of salt and pepper.
Taste and adjust—aim for bright and savory with a gentle garlicky kick.
Season the cod: Sprinkle the fillets with 1/2 teaspoon salt and 1/4 teaspoon pepper. Spoon 1–2 teaspoons of the lemon-garlic mixture over each fillet and rub lightly to coat.
Add cod to the pan: Pull the pan of veggies from the oven. Push the veggies to the edges to create four spaces.
Nestle the cod in the open spots. Spoon a little more of the lemon-garlic mixture over the veggies.
Roast to finish: Return the pan to the oven and roast 8–12 minutes, depending on thickness. Cod is done when it flakes easily and turns opaque.
Aim for an internal temperature of 130–135°F (54–57°C) for moist, just-cooked fish.
Final touch: Drizzle the remaining lemon-garlic mixture over the cod and veggies. Sprinkle with chopped parsley. Add extra lemon wedges on the side.
Serve: Plate the cod with a mound of veggies.
Spoon any pan juices over the top. Taste and add a last pinch of salt or squeeze of lemon if needed.