Preheat the oven to 375 ℉ and grease a large, shallow ovenproof dish.
Thinly sliced the fennel, reserving the green fronds.
Heat the butter and olive oil in a large frying pan and gently cook the fennel, onion, and garlic for 12 to 15 minutes or until softened but not browned.
Season with salt and freshly ground black pepper.
Stuff each fish with a heaping tablespoon of the fennel mixture and 1/4 of the fennel fronds.
Brush with extra virgin olive oil, squeeze lemon over the top, and season well.
Spoon the remainder of the fennel mixture into the oven-proof dish and sprinkle with half of the oregano.
Lay the fish on top of the fennel.
Sprinkle the remaining oregano over the fish and cover the dish loosely with foil.
Bake for 15 minutes or until just cooked through.
Garnish each serving with a wedge of lemon.