Cook the noodles according to the package directions, being careful to leave them al dente and not over cooked. drain the noodles in a colander and set aside.
Prepare the sauce by stirring together the soy sauce, water, brown sugar, chili garlic sauce, and sesame oil. Set the sauce aside.
Mince the garlic and grate the ginger. Use a large-holed cheese grater to grate the carrot (or julienne using a mandoline). Slice the green onions on a diagonal, separating the fleshy white portions from the green ends.
Heat the vegetable oil in a large skillet over medium heat. Once hot, add the ground beef, garlic, and ginger. Sauté until the beef is cooked through. Add the white portions of the sliced green onions and sauté for one more minute. Add the shredded carrots and sauté for one minute more (leaving the carrots slightly crunchy).
Add the drained noodles and the prepared sauce to the skillet. Stir until everything is coated in sauce and any extra moisture has been absorbed by the noodles. Turn the heat off and top with the green portion of the sliced green onions and fresh cilantro leaves.