Preheat the oven to 200°C/400°F/gas 6.
Slice the potatoes as thinly as possible (use a mandolin if you have one), then mix with 2 tablespoons of olive oil, the chopped garlic and thyme leaves. Season, then spread the mixture over a greased baking tray. Bake for about 15 minutes, until the potatoes are cooked.
Meanwhile, blitz the olives and half the chives with the remaining olive oil in a food processor to make a thick purée.
Season the fillets. Heat some oil in a frying pan until it is medium hot – the oil should be shimmering but not smoking – and fry the mullet for 2 minutes skin-side down, then turn over and fry for another minute. You want a crispy skin.
Divide the potatoes between four plates, pop two fillets on top of each mound and, using a teaspoon, drizzle the plate with the olive purée. Scatter the remaining chives over everything and eat immediately.