Peel and chunk potato (125 g), boil 10-15 min until tender, drain and mash smooth; cool and measure out 125g.
Mix flour (225 g), salt (1 1/4 tsp), sugar (4 tsp) and yeast (1 tsp) in a large bowl. Make a well, add olive oil (1 1/2 tbsp) and warm water (180 ml), mix with a spatula until no flour shows — sticky dough (add water by the tbsp if dry).
Fold and smear in the mashed potato (125 g) until evenly incorporated; shape into a ball. Cover and Rise 1: 30 min at 25°C until up 50%.
Oil a second bowl (2 tsp oil), scrape dough in, fold edges to centre 6 times, shape into ball. Cover and Rise 2: 30 min until up 50%.
Oil a 26.5x20x5cm metal pan (2 tbsp olive oil (4 tbsp)). Preheat oven to 220°C/430°F (200°C fan), 15 min minimum. Scrape dough in and stretch to fill base. Rise 3: cover, 40 min until dough fills pan and rises ~25-30%.
Drizzle surface with 2 tsp oil (4 tbsp), rub over, then poke fingers deep to the pan base all over to dimple.
Add toppings: for garlic-rosemary, gently poach garlic (5) in oil (180 ml) 10 min on low, strain, press on, sprinkle rosemary (2 1/2 tsp). For tomato, squish tomatoes (13) and press in, sprinkle oregano (3/4 tsp). For olive, press olives (17) in, sprinkle oregano (3/4 tsp).
Drizzle with remaining 2 tbsp olive oil (4 tbsp) into dimples, sprinkle sea salt flakes (1/4 tsp). Bake 25-30 min until deep golden and crisp, sides crusty. Turn out onto rack, rest 10 min before slicing. Serve warm.