Preheat your oven to 170°C.
Arrange mozzarella and tomato slices on plates and warm them in the oven for five minutes.
Blend basil, pine nuts, parmesan, and garlic in a food processor to a fine purée.
Gradually blend in 125ml of olive oil, adding more if a thinner consistency is desired.
Heat olive oil in a pan and fry the monkfish for 5 minutes until golden and cooked through.
Allow the fish to rest for a few minutes after removing from the heat.
Coat the monkfish in 3-4 tablespoons of the prepared pesto.
Place the fish onto the warm plates and drizzle with the remaining pesto and black pepper.