Preheat the oven to 400 degrees F.

Line a heavy large baking sheet with foil.

Oil the foil and the fish with 1 tablespoon of olive oil.

Place the red snapper atop the foil.

Sprinkle the fish cavity with salt and freshly ground black pepper.

Squeeze the juice of 1/2 lemon inside the fish cavity.

Fill the cavity with the chopped onion, chopped fennel bulb, and rosemary sprigs.

Bake until the fish is cooked through at the bone, about 40 minutes.

Meanwhile, squeeze the juice of the remaining 1/2 lemon into a small bowl.

Whisk in the chopped fennel fronds, chopped rosemary leaves, and minced garlic.

Gradually whisk in the remaining 3 tablespoons of olive oil.

Season the lemon sauce, to taste, with salt and freshly ground black pepper.

Using a sharp knife, separate the 2 fillets from the backbone.

Using a metal spatula, transfer the top fillets to a plate.

Lift the fish backbone from the bottom fillets (the backbone and head should come off together easily), and discard.

Using the spatula, transfer the remaining fillets to plates.

Sprinkle the fish fillets with salt and freshly ground black pepper.

Drizzle the lemon sauce over the fish and serve.