Pour the flour on a clean work surface. Make a deep well in the middle of the flour and crack the eggs in the center of the well. Using a spoon, gently break the yolks and stir the eggs to collect the flour around the edges. Stir in more and more flour until the entire pile of flour clumps. Then gather the clumps and knead into a ball. Knead aggressively for 5 minutes, until the dough becomes smooth and firm. Wrap the dough in plastic and allow it to rest while you prepare the veggies.
For the Vegetable Lo Mein Recipe:
Trim and slice all vegetables into thin bite-size pieces. Heat a large pot of salted water to boil the pasta and get a wok (or large skillet) out for the lo mein. Also set out a pan to hold the sauteed veggies.
Flatten the dough ball a little and cut it into 2-inch strips. Place the pasta roller attachment on the KitchenAid mixer and run each piece of dough through the roller to flatten. Lay each piece out on a floured surface. Then switch the attachment to the spaghetti cutter, and run each sheet of dough through the cutter to form thin noodles. Flour the noodles as they come through the cutter and lay them out on a floured surface. *If you don't have these attachments you can use a countertop pasta maker, or even roll the dough out flat and cut with a pizza roller.
After the noodles are ready, heat the wok over high heat to stir fry the veggies. Place 1-2 teaspoons of oil in the wok and wait until it smokes. Then place one vegetable at a time in the wok and stir fry for 1-2 minutes moving constantly. Scoop the veggies out and place in the holding pan, then repeat with the next vegetable. You want the veggies to be bright, crisp and barely cooked, not soft and flimsy. This should take 5-8 minutes total.
Once all the veggies are cooked and moved to the pan, turn the heat to medium and place the sesame oil in the skillet, followed by the garlic and ginger. Saute for one minute, then add the soy sauce, black vinegar, fish sauce, water, and cornstarch. Whisk immediately to incorporate the corn starch then allow the sauce to thicken a little.
Start the sauce, then immediately drop the homemade noodles in the boiling pot of water. They should take only 2-3 minutes to cook. Drain well.
Once the sauce thickens, pour the drained pasta and all the veggies back into the wok. Toss and simmer another minute or two to thoroughly coat and season the pasta. Serve warm.