Preheat the oven to 425°F (220°C) and line a sheet pan with parchment paper or foil.
Pat the branzino completely dry inside and out with paper towels.
Make 3 to 4 diagonal slashes on each side of the fish, about half an inch apart.
Rub 2 tablespoons of olive oil over both fish, inside and out, then season with salt, pepper, and paprika.
Fill each fish cavity with lemon slices, garlic slices, thyme, and parsley.
Arrange the fish on the sheet pan, drizzle with remaining olive oil, and top with extra lemon slices.
Roast for 18 to 22 minutes, until the flesh is opaque and flakes easily and the internal temperature reaches 145°F (63°C).
Let the fish rest for 3 minutes before serving with extra lemon wedges.