How to Make It
Preheat the oven to 425°. In a medium bowl, mix the butter with the capers, lemon juice and parsley and season with salt. Keep at room temperature.
Season the branzino cavities with salt and stuff 2 lemon rounds and 1 rosemary sprig in each. Season the fish with salt.
In a large, nonstick, ovenproof skillet, heat 2 tablespoons of the olive oil until shimmering. Add 2 of the branzino and cook over high heat until the skin is browned and crisp, about 3 minutes per side. Transfer the fish to a large rimmed baking sheet. Repeat with the remaining 1 tablespoon of olive oil and 2 stuffed branzino. Roast the fish in the oven for about 10 minutes, until just cooked through.
Serve whole or filleted, passing the caper butter at the table.