Preheat your oven to 400°F (200°C). On a large rimmed baking sheet, toss the thinly sliced potatoes and fennel with 2 tablespoons of olive oil, half the minced garlic, salt, and pepper. Spread them out in a single layer to ensure they roast evenly. Place the baking sheet in the oven and roast for 20 minutes, or until the potatoes are just starting to turn golden and tender when pierced with a fork.

While the vegetables roast, pat the cod fillets dry with paper towels. Season both sides with salt, pepper, and the dried oregano. In a small bowl, whisk together the remaining tablespoon of olive oil, the remaining garlic, and the lemon juice. Remove the baking sheet from the oven and move the vegetables slightly to make room for the fish. Place the cod fillets on top of the vegetables. Drizzle the lemon-garlic oil over the fish and top each fillet with a lemon slice.

Return the baking sheet to the oven and roast for another 10 to 12 minutes. The fish is done when it is opaque throughout and flakes easily with a fork. If you are using olives or capers, scatter them over the pan during the last 5 minutes of cooking. Once finished, remove from the oven and sprinkle fresh parsley over everything. Serve immediately, drizzling any pan juices over the fish.