Preheat the oven to 220C/430F/Gas 7.
For the pizzetta bases, in a jug, mix together the water, yeast, sugar and olive oil until well combined (this is the starter).
Sift the flour and salt into a large bowl. Make a well in the centre, then pour the starter mixture into the well and add the chopped olives. Stir until the mixture comes together as a dough and is well combined.
Turn out the dough mixture onto a lightly floured work surface and knead for 3-4 minutes until smooth.
Divide the dough into 20 equal portions and roll into balls (each portion should be about the size of a tennis ball). Place the dough balls onto a baking tray and cover with a damp cloth, then set aside in a warm place for 18-20 minutes, or until the balls have doubled in size.
On a lightly floured work surface, flatten each ball of dough with your hands to form pizzetta bases that are 2.5cm/1in thick and 5cm/2in in diameter. Set aside.
For the tomato sauce, heat the oil in a pan over a medium heat. Add the chopped chorizo and fry for 3-4 minutes, or until the chorizo is fragrant and crisp.
Add the tomatoes and garlic, stir well and bring the mixture to a simmer. Continue to simmer over a medium heat for 25-30 minutes, or until the tomatoes have broken down. Add the basil leaves and sugar. Season, to taste, with salt and freshly ground black pepper.
For the topping, spread half a tablespoon of the tomato sauce all over each of the pizzetta bases. Sprinkle over the topping ingredients.
Transfer the pizzette to a hot oven and bake for 8-10 minutes, or until the bases are crisp and golden-brown, the cheese has melted and the topping ingredients have softened and coloured.
To serve, slice the pizzette and place a handful of rocket salad alongside.