Pour the water into a large bowl with the olive oil and salt. Add gradually the two flours, stirring with a fork.
When the dough will be too hard to be mixed with a fork, move the dough onto a wooden board and knead by hand to incorporate all the flour. Knead the dough until smooth. You might need more flour if too sticky or more water if you are not able to collect all the flour. Let the dough rest on the wooden board covered by the bowl for about half an hour.
While the dough is resting, prepare the sauce for the pici. Thinly slice the leek, both the white part and the green part.
Collect the leek in a pan, drizzle with some extra virgin olive oil and season with a generous pinch of salt. Cook the leeks on low flame for about ten minutes, until they are soft.
Add now the cleaned, peeled and diced butternut squash and the sausage, after you have removed the case, cut into small pieces. Stir and cook on low flame for about twenty minutes, until the squash is soft, almost a cream.
Now season with salt and pepper and add the cubed Pecorino. Cook the sauce until the pecorino starts to melt, then turn off and set aside.
Now work on the pici again. Roll out the dough on the board with a rolling pin to a thickness of about half a centimetre. Do not use flour, it won't stick. Brush with olive oil to prevent it from drying.
Cut the dough with a pizza wheel into strips not larger than a centimetre and get ready to make pici. Roll the pici as they were play doh worms. Children are great at it.
Keep beside you a bowl of semolina and corn flour and dip your picio in the bowl as you go, then wrap it around your hand and put it aside on a tray.
Cook the pici in salted boiling water a few minutes, drain them al dente and pour them into the pan with the seasoning. Toss with some cooking water, stir to melt the cheese and serve immediately.