To make the fennel slaw: Carefully pick off the fennel fronds and set them aside. Using a mandoline, shave the fennel bulb into ⅛-inch slices.
In a medium bowl, whisk together the lemon juice, vinegar, garlic, shallot, and oil. Season with salt and pepper and add the mint. Toss all but a few pieces of the shaved fennel and almost all of the fennel fronds with the vinaigrette and let sit for 1 hour.
To make the branzini: Preheat the oven to 450°F. Spread 2 tablespoons of the oil over a large rimmed baking sheet to fully coat it.
Rinse the branzini well and pat dry with paper towels. Place the fish on the prepared baking sheet. Season the cavity and exterior of each fish with salt and pepper. Alternating slices of the citrus, stuff the cavity with 2 lemon slices, 2 orange slices, and a few slices of the reserved fennel and fennel fronds. Place a few slices of lemon over the top of each fish. Drizzle with the remaining 2 tablespoons oil and roast until cooked through, about 15 minutes.
Turn the oven to broil and broil for 2 minutes, just to give it an extra hint of golden color.
Transfer the fish to a serving platter and serve topped with the fennel slaw and the lemon wedges alongside.
Serves 4 | Total Time: 1 hour and 30 minutes (Prep: 10. Cook 17 to 20.)