Put the fennel, onion, courgette and olive oil in a shallow roasting tin and mix together, seasoning with salt and pepper. Place on the upper rack of the halogen oven.
Set the temperature to 200°C (392°F) and cook for 10 minutes, stirring a couple of times, until the vegetables have softened. Stir in the herbs and olives.
Season the monkfish fillets with salt and pepper, and nestle them down into the vegetables. Mash the drained anchovy fillets in a bowl, then add their oil, the garlic and a little seasoning. Spoon the dressing over the fish. Cook for about 15 minutes until the monkfish is cooked through. Serve scattered with basil leaves.