For the taglierini pasta, place the '00' flour, some salt and freshly ground black pepper, egg yolks, eggs and oil into a food processor and process for one minute, or until the mixture comes together to form a smooth dough. Tip the dough out into a bowl, cover with cling film and chill in the fridge for 30 minutes.
After 30 minutes, remove the dough from the fridge and turn out onto a floured work surface. Divide the dough into two equal pieces.
Flour the pasta machine and, starting at the lowest (thickest) setting, feed one piece of the dough through the machine, turning the handle with one hand and holding the dough as it comes through the machine with the other. Change the setting on the pasta machine to the next-thickest setting, flour it again and feed the pasta sheet through the machine again, as before.
Repeat this process 3-4 more times, flouring the machine and changing the setting each time. The pasta should be quite thin, but still easy to handle without tearing. Don't be tempted to skip settings or the dough may tear. Repeat with the other piece of dough until you have two sheets of pasta (cover the first sheet with a clean tea towel while you work on the second one, to prevent it from drying out).
Once the pasta sheets have reached the ideal thickness, trim the edges slightly. Attach the taglierini cutter attachment to the pasta machine, flouring it well. Feed the sheets of dough through the machine once again, cutting them into 3mm-thick strands of taglierini. Dust the pasta with flour, place on a tray, cover and place in the fridge overnight.
Preheat the oven 150C/300F/Gas 2.
For the squid and oven-roasted tomato sauce, place the tomato halves onto a baking sheet, cut-sides up, and drizzle with half of the olive oil and season with salt and freshly ground black pepper. Roast in the oven for 1½ hours, or until the tomatoes are soft and slightly dried out. (You can prepare the tomatoes a few days in advance, storing them in olive oil in a sterilised jar. Keep in the fridge until needed.)
Heat a large frying pan and add 1 tablespoon of the remaining olive oil. Fry the shallots and garlic 2-3 minutes, or until softened. Turn up the heat and add the white wine, scraping up any browned bits from the bottom of the pan with a wooden spoon to deglaze. Simmer for 3-4 minutes, or until the liquid has reduced in volume by one-third. Add the roasted tomatoes to the pan, along with the basil leaves.
Heat a medium frying pan and add the remaining olive oil. Add the squid rings and tentacles and fry for 2-3 minutes, or until just-cooked.
To serve, bring a large pan of salted water to the boil, add the taglierini and cook for 2-3 minutes, or until al dente. Drain the pasta and add to the pan with the tomato sauce. Add the cooked squid and mix well. Pile the pasta onto serving plates and garnish with a few basil leaves.