Put the flour on a large wooden working surface, make a well in the centre of the flour and add the salt and a tablespoon of extra virgin olive oil. Now add the water little by little, stirring with your hands until a dough is formed. The required quantity of water may be different each time.
Knead the dough until firm and smooth: you'll need about 10 minutes.
Flatten the dough just like making pizza, brush it with a generous dash of extra virgin olive oil and cover with clingfilm.
Let it stand at room temperature from 2 hours up to a whole night.
Roll out the dough into a thick sheet (at least 5 mm), then use the pici rolling pin or a knife to make deep cuts in it, about 5 mm large. Then, take out one noodle after the other, stretching and rolling them with your hands to make a kind of thik spaghetti.
Place the pici on a sheet tray dusted with flour and set aside to dry. Boil them in steaming salted water for about 10 minutes, then drain them and season as you prefer.
Pour the extra virgin olive oil in a thick bottomed pan and add the garlic cloves, peeled and crushed.
Cook on very low heat for about 5 minutes, letting the garlic infuse, until it gets lightly golden.
Pour in the tomato pulp and stir. Cook on low heat for about 10 minutes.