Trim the tops from the beetroots and boil them in their skins until you can insert a thin knife into them easily - this should take approximately 40-45 minutes.
Drain the beetroots. Let them cool, then peel them and blitz to a puree in a food processor. Whisk together the eggs, egg yolks, beetroot puree and salt.
Gradually add flour to the beetroot mixture until you have a firm dough.
Knead the dough for 5-10 minutes until it’s silky and smooth. If it’s too wet, add more flour 1 tbsp at a time until you can knead easily with just a small amount of flour on your worktop.
Put the dough into a plastic bag and put to one side for 30 minutes. You can put the dough in the fridge overnight, but bring it to room temperature by removing it from the fridge one hour before you use it.
Preheat your oven to 180C and lay the walnuts out in a single layer on a tray. Roast the nuts for 8-10 minutes, turning once or twice, until fragrant and golden brown.
Remove the tray from the oven and tip the nuts off it onto your chopping board. Let them cool slightly before roughly chopping and putting to one side.
Bring a large pan of water to the boil - the bigger the better. Add 1/2 tsp salt.
Remove the dough from the plastic bag and knead it a few times to make it soft and pliable.
Shape your chosen pasta shape.
Gnocchetti Sardi: take a marble sized piece of pasta, and slide it down the back of a fork with your thumb, allowing it to curl over as you push it down. Dust some flour on a plate or tray and sit the gnocchetti there while you shape the rest of the dough.
Casarecce: take a marble sized piece of pasta and roll it into a 6 cm tube. Slide a wooden skewer across the width of the pasta to create a curl across it.
Farfalle - roll out one quarter of the pasta using a rolling pin until it’s 1mm thin. Dust with flour, then use a ravioli cutter or crimped scissors to cut out rectangles 2 cm x 4 cm. Use your index finger and thumb to pinch together the middle of the ‘bow tie’. Put the shaped pasta on a lightly floured tray while you shape the rest.
Fusilli: take a marble sized piece of pasta and roll it into a 10 cm tube. Roll the thin end of a round chopstick diagonally across the pasta, winding the pasta around it as you go. Gently slide the pasta off the chopstick and let it dry slightly while you shape the remaining dough.
Orecchietti - take a marble sized piece of dough and slide a butter life blade across it, to flatten it out. Turn the pasta shape over and slightly invert it, to create the authentic orecchiette shape.
Cook batches of the pasta in boiling water for 1.5 to 2 minutes, or until it rises to the top. Drain and immediately toss with the olive oil.
Serve with crumbled Roquefort, chopped toasted walnuts and baby leaves.