Special equipment: a pasta machine with a fettuccine attachment, optional
Pulse together the cilantro, avocado and 1/2 cup water in a food processor until completely smooth, scraping the sides if needed, about 2 minutes. Add the flour, then pulse until all of the liquid is absorbed and a large, soft dough ball forms (it's okay if there are some crumbles, the dough will come together when it's kneaded).
Transfer the dough to a work surface dusted with flour and gently gather into a ball, sprinkling with flour as needed to avoid the dough sticking to your hands. Take care not to overwork the dough.
Dust a baking sheet with flour. Cut the dough into 4 equal pieces. Cover with plastic wrap. Dust the work surface with flour again and roll 1 piece of dough out to about 1/16-inch thick in a roughly 18- by 6- inch rectangle. Cut into 1/4-inch strips using a paring knife or pizza cutter. Transfer to the prepared baking sheet and sprinkle with more flour to keep the noodles from sticking to each other. Cover with plastic wrap and roll out and cut the remaining dough. You can also use a pasta maker to roll out your dough and cut into noodles with the fettuccine attachment.
Bring a large pot of salted water to a boil. Whisk together the vinegar, sesame oil and ginger in a large bowl. Add the carrot and cabbage, toss to combine and let sit for a few minutes until the dressing becomes magenta.
Shake off the excess flour from the pasta, drop into the boiling water and cook until tender and no longer floury (it should rise to the top of the pot), 1 to 2 minutes. Drain the pasta and add to the bowl along with the cabbage, carrots and toss to coat well. Season with salt and pepper. Garnish with cilantro, sesame seeds and Asian garlic-chile sauce.
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