Mix flour, salt, yeast, 300ml warm water, and olive oil in a large bowl.
Knead the dough for five minutes until elastic.
Cover with cling film and allow to prove for one hour.
Divide dough into four balls and roll out to 5mm thickness on a floured surface.
Place on a floured baking tray and prove for another 30 minutes.
Fry shallots and garlic in oil for 4 minutes, then add tomatoes, sugar, and chopped basil.
Simmer for 20 minutes until thickened, season, and let cool.
Preheat the oven to 220°C.
Place a heavy baking tray or pizza stone in the oven to preheat.
Spoon a thin layer of cooled tomato sauce over the pizza base.
Scatter sliced mozzarella and piquillo peppers on top.
Transfer the pizza onto the preheated tray or stone.
Cook for 10 minutes until the base is crisp.
Arrange pata negra, rocket, and basil leaves on the hot pizza.
Fry padron peppers in olive oil and salt for 3 minutes until golden.
Serve the pizza immediately with the fried peppers on the side.