Preheat the oven to 170C/325F/Gas 3.
For the salad, lay the slices of mozzarella and tomato onto four serving plates, alternating the mozzarella and tomato slices in a circle around the edges. Place into the oven to warm through for five minutes.
For the pesto, place the basil, pine nuts, parmesan and garlic into a food processor and blend to a fine purée. Add 125ml/4½fl oz of the olive oil and blend again until well combined. If the pesto is too thick, add the remaining olive oil to thin it out. (You may not need all of the olive oil.) Set aside.
For the monkfish, heat the olive oil in a frying pan and fry the fish on all sides for 4-5 minutes, or until golden-brown and cooked through. Remove the pan from the heat and allow the fish to rest for a few minutes.
Drizzle 3-4 tablespoons of the pesto over the fish and mix well to coat.
To serve, carefully remove the plates of mozzarella and tomato from the oven using oven gloves. Spoon the monkfish onto the centre of the plates, then drizzle the remaining pesto around the mozzarella and tomato. Garnish with a few fresh basil leaves and season with some freshly ground black pepper.