Dissolve the yeast in the water. Add the oil, salt and flour (reserve some of the flour for later). Knead the dough well. Let the dough rise in a warm place for approx. 30 min.
Combine the tomato purée with the onion, water, oregano and salt.
Tip the dough out onto a floured surface and knead thoroughly. Add the rest of the flour as needed. Divide the dough into 4 parts and roll out each one into a thin, round pizza base (approx. 22 cm in diameter). Place the pizza bases on 2 pieces of baking parchment. Spread tomato sauce on the bases and sprinkle with cheese. Coat the potatoes in oil and place on the pizza bases, overlapping slightly. Sprinkle with salt and bake 2 of the pizzas in the middle of the oven. Take them out after approx. 15 min at 250°C (conventional oven). Sprinkle with half of the peperoni, then finish baking the pizzas. Garnish the 2 hot pizzas with fresh oregano leaves and serve immediately (½ a pizza per person). Meanwhile, bake the last 2 pizzas.
All 4 pizzas can be baked in a fan oven at the same time at 225°C. Instead of making tomato sauce yourself, you can use a ready-made pizza sauce – approx. 250 ml.