stand mixer with pasta attachment or hand-cranked pasta machine
Preheat the oven to 500 degrees F. Cut a thin slice from the stem end of the tomatoes and score the other end by cutting a small "x." Place the tomatoes in a small bowl, toss with enough olive to coat and season lightly with salt and pepper. Stand the tomatoes up on their cut sides in a baking dish and place in the oven to cook until the skins are lightly blistered, about 6 minutes. Set aside to cool.
Meanwhile, set up a pasta roller attachment on a stand mixer (or secure a hand roller to the side of your work surface) and set it on the widest setting. Lightly dust a baking sheet and work surface with semolina and roll out your dough with a rolling pin until it is thin enough to pass through the pasta roller. Turn on the pasta roller and pass the dough through once, then fold in half, dust with semolina flour, and put through the roller again. Keep dusting lightly with semolina flour as needed if the dough seems sticky or damp. Go the next setting and pass the pasta through the roller (without folding). Go to the third setting and repeat. Go to the fourth setting and repeat (you will have rolled the dough to a medium thickness; it should not be translucent).
Once the pasta is rolled, cut the long sheet into 10- to 12-inch sections, stacking them on top of each other with a dusting of semolina in between. (You should end up with 4 or 5 sections.) To cut by hand, fold each sheet in half, then in half again. With either of the folded ends facing you, cut very thin slices to achieve a thin noodle. To cut with the pasta machine, use the spaghetti roller attachment and put each section of rolled dough through the machine one at a time. Put the cut spaghetti on the prepared baking sheet; toss to coat with semolina and roll into 4 to 5 nests. Each nest is about one serving.
Bring a large pot of salted water to a rapid boil.
Remove the skins from the tomatoes with your hands or a paring knife (if they have been properly roasted the skin should lift easily). Squeeze out the juice and seeds, then break up what is left of the tomato flesh with your hands and transfer to a bowl.
Put the oil, garlic and chiles in a large skillet over medium heat. Cook, stirring occasionally, until the garlic cloves are lightly browned, about 1 minute; add the tomatoes and any juice that has accumulated in the bowl. Season with salt and bring to a boil, then reduce the heat to low and hold for the pasta.
Drop the pasta into the boiling water and stir immediately. Leave the pasta to cook, stirring occasionally, until al dente, about 2 minutes.
Transfer the cooked pasta to the pan with the sauce; toss and simmer until well combined. Add the basil and Parmesan and toss well. Serve, drizzle with olive oil and more Parmesan.
Mound the flour in the center of a clean countertop or cutting board. Make a well in the center of the flour 3 to 4 inches wide.
Crack the eggs into the well and add a pinch of salt. Using a fork, break the yolks and begin to beat the eggs as you would if making scrambled eggs.
Continue stirring the eggs with a fork in large circles, slowly incorporating the flour. When the eggs form a thick mass and become difficult to stir, about 3 minutes, fold the loose flour from the edges into the pile with a bench scraper and knead until a smooth dough forms. Discard any excess flour.
Shape the dough into a flat disk, wrap tightly with plastic wrap and set aside to rest for 20 minutes before rolling. If waiting more than 1 hour, refrigerate or freeze the dough. The dough will keep refrigerated for up to 24 hours.
If you don't have semolina, you can use 10 ounces of only "00" or all-purpose flour instead of 7 ounces flour and 3 ounces of semolina flour.
You can substitute 6 large egg yolks for the 3 whole eggs for a richer pasta dough.