Dissolve the yeast in half of the warm water with the sugar. Set aside until foamy, about 5 minutes.
Place flour and semolina in a large bowl. Make a well and add oil, yeast and the remaining water. Mix to make a sticky dough, adding more water if needed. Transfer onto a floured surface; add salt and knead for 8 to 10 minutes or until smooth and soft.
Lightly oil a bowl; place the dough in the oiled bowl, cover with a clean, damp drying cloth. Place the bowl in a cold oven with the light on. Let rise for 1 hour.
Gently punch down the dough; return the bowl to the cold oven to rise for another hour.
Preheat the oven to 250 C / Gas 9. Preheat a pizza baking stone until hot.
Divide the dough into 4 equal pieces. Roll out each piece of dough with your hands, stretching it a bit at a time. Make 4 (20cm) pizza bases and place the first one on the baking stone. Drizzle with some olive oil and bake for 4 minutes.
Remove the pizza base from the oven; add 1/4 of the grated mozzarella, 4 pieces of tomato and bake for 5 minutes.
Arrange 3 anchovies on top of the pizza and cook for 5 minutes or until the edge of the pizza is golden. Add 1/4 of the buffalo mozzarella cubes and serve.