Preheat the oven to 260 C (500 F) with a pizza stone inside. Stretch dough to 30 cm (12 inch) round on a floured surface.
Spread tomato sauce evenly, leaving a 1 cm (1/2 inch) rim. Sprinkle 150 g (5 oz) mozzarella, then reserve remaining cheese for later.
Slide pizza onto the hot stone and bake 8-10 minutes until crust is blistered and cheese is bubbling.
Meanwhile, parboil potatoes for 5 minutes, drain, and cool. This softens the interior and primes fries for crisping.
Heat oil to 180 C (360 F) in a deep fryer or pot. Fry potatoes in batches 3-4 minutes until pale golden, drain, then double fry at 200 C (390 F) for 2 minutes until deep golden and crisp.
Toss fries with salt, pepper, and a light drizzle of olive oil. Add a sprinkle of grated Parmesan while hot for umami and sheen.
Remove pizza from oven, top with remaining mozzarella, then arrange fries over one half for a layered look, or pile them beside the pizza for contrast.
Garnish with fresh basil or parsley, crack black pepper, and finish with a final dusting of Parmesan. Serve hot for best texture contrast.