Put the flour in a large bowl and stir in the yeast and a pinch of salt. Make a well in the centre and add 1/2 cup of tepid water and 3 teaspoons of the olive oil. Mix with a round-bladed knife until the mixture forms a soft dough, adding a little more water if it feels too dry. Turn the dough out onto a lightly floured surface and knead for 5 minutes until the dough is soft and supple. Place in a lightly greased bowl, cover with a tea towel and leave to rise in a warm, draught-free place for 1 hour, or until doubled in size.
Meanwhile, heat the remaining olive oil in a deep frying pan. Add the onions and cook gently over a moderate heat for 5 minutes without letting them colour. Add the bay leaf and oregano, then season to taste. Cover and continue to cook gently, stirring occasionally for about 35 minutes until cooked but still transparent.
Preheat the oven to 230 degrees C. Add the chopped anchovies to the onions. Let them cook gently for 2–3 minutes, then remove the pan from the heat. Remove the bay leaf. Lightly oil two baking trays.
Turn out the risen dough onto the floured surface, and punch it down, then knead very lightly. Divide into four, then roll out to make four rounds, each about 15cm in diameter. Put two rounds on each baking tray. Spread the onions on top to within 1cm of the edges.
Bake for 10 minutes, then scatter the olives over the pizzas and bake for a further 5 minutes, or until the pizza bases are lightly risen and golden. Garnish with basil, then serve.