Make the pasta: Sieve the flour into a food processor and add the eggs, egg yolks, salt and oil. Pulse the mixture until it looks like fine breadcrumbs then mix on a higher speed until it starts to come together. If it looks too dry, add another egg yolk. Dust a clean worksurface with flour and tip out the pasta dough. Divide the dough in half (this will make it easier to work with) and knead each half by hand for about 5 minutes until completely smooth and shiny. Wrap each ball of dough in cling film and chill for 30 mins – 1 hour. Remove from the fridge and pass through a pasta machine, starting at the thickest setting and working down to the thinnest setting. The pasta is then ready to make into tortellini.
Make the filling: Boil the potatoes whole in salted water until tender. Leave to cool slightly then scrape off the skin. Discard the skin and pass the potatoes through a potato ricer. Add the mint, Pecorino and nutmeg, mix together with a fork and taste. Adjust seasoning if necessary and leave to cool before using.
Make the tortellini: Using a 5cm fluted biscuit cutter, cut out as many discs as you can from the rolled sheets of pasta. Using a teaspoon and your finger, place a very small amount of the filling in the middle of each disc. Brush a little water round the edge of each disc. Fold the disc in half over the filling so that the top and bottom edges do not quite meet. Press to seal. Wrap the half moon shape around your index finger and pinch to seal. If this gets too complicated you can leave them as semi-circles and call them agnolotti! Place the made pasta shapes on a floured tea towel until ready to cook.
To cook: Bring a large pan of salted water to the boil and place in the pasta shapes. Lower the heat to a simmer. The pasta will rise to the top after about 30 seconds but will probably require 3-4 minutes cooking. test one to see if it is al dente. Drain.
To serve: This type of pasta goes well with a homemade tomato sauce with garlic and dried chilli or just drizzled with really good extra virgin olive oil and more grated pecorino.