Preheat your oven to 400°F (200°C).
Rinse the branzino inside and out with cold water, pat dry with paper towels.
Season the cavity of each fish with salt, pepper, and a sprinkle of thyme.
Stuff the cavity of each branzino with orange slices, lemon slices (reserve some for garnish), and a portion of the minced garlic.
In a roasting pan, lay the sliced fennel as a bed for the fish.
Drizzle the fennel with half of the olive oil, season with salt, pepper, and red pepper flakes, and toss to coat.
Place the branzino on top of the fennel bed.
Drizzle the remaining olive oil over the branzino and sprinkle with the remaining thyme and garlic.
Roast in the preheated oven for about 25-30 minutes, or until the fish is opaque and flakes easily with a fork.
Remove from the oven, and drizzle with fresh lemon juice and garnish with parsley and fennel fronds.
Serve immediately with additional lemon and orange slices on the side.