Make the pizza dough. Sift the flour into a bowl and stir in the salt and yeast. Make a well in the middle and gradually work in the measured water and the oil until the mixture comes together in a ball. Transfer to a lightly floured surface and knead for 8—10 minutes or until the dough is smooth. Place in an oiled bowl, cover with clingfilm and leave to rise for 1 hour until doubled in size.
Knock the air from the dough and cut in half. Roll one piece out on a floured surface to form a 23 cm (9 inch) round. Lightly spray a heavy-based frying pan with oil and press the dough into the base. Spread half the pesto over the dough and top with half the tomatoes, mozzarella and olives, some salt and pepper and a drizzle more oil.
Place the pan on a moderately hot barbecue, cover with the barbecue lid or a wok lid and cook for 10—12 minutes until the dough is crisp underneath and the cheese melted. Carefully slide the pizza out on to a board, garnish with half the basil leaves and serve hot. Make the second pizza.