Preheat your oven to 220°C/430°F (200°C fan) and line a large baking tray with parchment paper.
Trim the fins from each fish with kitchen scissors, then cut three deep slashes on both sides of the fish, slicing right down to the bone.
Season the inside cavity of each fish with a pinch of salt and pepper, then stuff with garlic slices, parsley, and dill, layering the lemon slices over the herbs.
Tie each fish in three spots with kitchen string to keep the stuffing secure, then season the skin all over with the remaining salt and pepper, drizzle with olive oil, and rub it into the skin and slashes.
Place the fish on the prepared tray and bake for about 20 minutes, or until the thickest part of the flesh reaches 55°C/131°F or flakes easily away from the bone with a knife.
Remove the fish from the oven, transfer to a serving platter, and let it rest for 5 minutes while you make the butter sauce.
Melt the butter in a small saucepan over medium-high heat, stir in the garlic, and cook for 45 seconds to 1 minute until fragrant, then remove from heat and stir in the dill.
Serve the baked fish warm with the garlic and dill butter on the side, or pour the sauce over the fish just before serving.