Sift flour and salt onto a clean work surface. Shape the flour into a round mound. Make a well in the centre. Crack eggs into the well. Use a fork to lightly whisk the eggs. Gradually blend a little of the flour into the egg mixture. Continue to gradually draw the flour into the centre until the mixture forms a dough. Knead firmly, turning frequently, for 10 mins or until smooth and elastic. Cover with plastic wrap. Place in the fridge for 1 hour to rest.
Divide dough into 4 equal portions. Cover each portion with plastic wrap. Secure a pasta machine to the side of the work surface. Adjust rollers to the widest setting. Shape 1 dough portion into a flat rectangle and use a rolling pin to flatten slightly. Roll through the machine. Dust with extra flour. Fold in the shorter sides of the dough to meet in the centre to form a smaller rectangle. Feed through the machine again. Repeat 6 times.
Reduce roller setting by 1. Roll dough through the machine. Continue reducing the setting and rolling until you reach the second-last setting and the pasta is about 1mm thick. Spread pasta sheet over a clean work surface dusted with flour. Sprinkle with flour and loosely roll up. Repeat with remaining dough.
Use a large sharp knife to cut the pasta sheets crossways into 2cm-wide ribbons and lightly dust with flour.
Meanwhile, to make the basil pesto, process the basil, parmesan, pine nuts and garlic in a food processor until finely chopped. With the motor running, gradually add the oil in a thin, steady stream until combined.
Cook the pasta in a large saucepan of salted boiling water for 2-3 mins or until tender. Drain well. Return to pan and add the pesto. Toss to combine. Divide among serving bowls. Top with shaved parmesan and serve immediately.