Preheat the oven to 200°C conventional oven/ 180°C fan-forced (400° Fahrenheit/Gas 6).
Cut off and reserve a few of the freshest looking fennel fronds. Trim the fennel bulbs by removing any green stalks. If the base of the fennel bulb is a little brown, cut a thin slice off. Use a vegetable peeler to remove any brown parts from the sides of the fennel. Cut the fennel bulb in half, then into thin slices, keeping them joined at the root. Use a mandolin or very sharp knife to thinly slice the potatoes (the same thickness).
Line a baking dish with baking paper. Arrange a layer of potato and fennel slices at the base of the baking dish. Drizzle half of the olive oil over the potato and fennel layer and season with salt and pepper to taste.
Cut 3 slashes in the thickest part of the snapper (sea bream) and season cavity with salt and pepper. Lay lemon slices, garlic, rosemary, half of the thyme and reserved fennel fronds in the cavity of the snapper. Arrange the snapper on top of the potato and fennel layer. Sprinkle the remaining thyme leaves over the fish, potatoes and fennel. Drizzle olive oil over the fish, and season with salt and pepper.
Bake for 30 minutes or until just cooked through (the flesh of the fish should be flaky and the dorsal fin will pull out easily). Remove and discard herbs and garlic from the fish cavity.
Place snapper, potato and fennel slices on a serving platter. Add lemon wedges to the platter. Serve immediately – buon appetito.