First make the fresh pici. Mix the flour and salt in a large bowl, then pour onto a pastry board or other work surface. Make a well with your fingers in the centre. Crack the egg into this well. Gradually mix the flour and egg, adding water a little at a time until the dough is firm but flexible. You may not need to use all of the water.
Knead the dough until well blended and it springs back to the touch.
Lightly dust a rolling pin with flour, and roll out the dough until it is about ½-1cm/¼-½in thick. Leave for 20 minutes to rest.
Cut the dough into 1cm/½in wide strips with a sharp knife. Hand-roll the strips into thick, spaghetti-like strands. These should be about 3mm/eighth inch wide.
To cook the pici, bring a large saucepan of salted water to the boil. Add the pici and cook for about 10-12 minutes. The exact cooking time will depend on the width of the strands.
Meanwhile, make the sauce. Heat the olive oil in a large saucepan. Add the garlic and allow it to flavour the oil. Add the breadcrumbs and the salt and freshly ground black pepper. Sauté for 2-5 minutes, stirring frequently, until the breadcrumbs are golden brown
Drain the pici and add to the breadcrumb mixture. Add the parsley and parmesan and toss to mix.
Divide the mixture between individual pasta bowls. If you like, add extra grated parmesan or olive oil to serve.