Preheat the oven to 450°F (230°C). Line a rimmed sheet pan with parchment and brush lightly with olive oil.
Pat the branzino very dry inside and out with paper towels.
Score 3 diagonal slashes on each side of each fish, cutting through the skin and about ¼ inch into the flesh.
Rub the fish with olive oil and season with salt, black pepper and red pepper flakes, working seasoning into the slashes.
Stuff each cavity with lemon slices, garlic slices, rosemary and thyme sprigs.
Roast 18 to 22 minutes, until the skin is golden and crisp and the flesh flakes easily.
Rest 3 minutes on the pan, then transfer to a platter.
Scatter with chopped parsley and serve with lemon wedges, filleting at the table along the backbone.