Preheat your oven to 400°F (200°C). Line a baking sheet with parchment paper or lightly grease a 9×13-inch baking dish to prevent sticking and make cleanup easier.

Place the red snapper fillets or whole snapper on a plate or cutting board. Use paper towels to pat the fish dry on all sides so the seasoning adheres well. If using a whole snapper, make 3–4 diagonal slashes on each side with a sharp knife to help it cook evenly and absorb flavor.

In a small bowl, whisk together the olive oil, minced garlic, lemon juice, lemon zest, salt, black pepper, dried oregano, dried thyme, and smoked paprika until well combined and fragrant.

Place the snapper in the prepared baking dish or on the lined sheet pan. Spoon the marinade over the fish and use clean hands or a pastry brush to coat thoroughly. For fillets, coat the tops and sides; for a whole snapper, rub the marinade over the entire fish, inside the cavity, and into the slashes. Let rest at room temperature for 10–15 minutes while the oven finishes preheating.

Scatter the halved cherry or grape tomatoes, sliced olives, and capers around and slightly on top of the fish. Drizzle any remaining marinade over the vegetables. Tuck lemon slices on top of the fillets or around the whole fish and sprinkle with chopped parsley, or reserve the parsley for serving.

Transfer the pan to the 400°F (200°C) oven. For fillets, bake 12–16 minutes, depending on thickness. For a whole snapper, bake 20–25 minutes. The fish is done when the flesh is opaque, flakes easily with a fork, and an instant-read thermometer in the thickest part registers about 130–135°F (54–57°C). Avoid overbaking.

As the fish is almost done, or immediately after removing it from the oven, drizzle the melted butter evenly over the top to create a rich garlic-butter finish. Let the fish rest for about 5 minutes to retain its juices.

Sprinkle with additional fresh parsley and serve with extra lemon wedges. Spoon the roasted tomatoes, olives, capers, and pan juices over the fish when serving.