Fill a large pot with lightly salted water and bring to a rolling boil over high heat. Once the water is boiling, stir in the noodles and return to a boil. Cook the noodles uncovered, stirring occasionally, until the noodles have cooked through but are still firm to the bite, 4 to 5 minutes. Rinse with cold water and drain well in a colander set in the sink. Toss noodles with 1 teaspoon of sesame oil. Set aside.
Whisk soy sauce and sugar in a small bowl. Set aside.
Heat the vegetable oil in a frypan over medium-high heat. Stir in the garlic, onion, carrots and asparagus; cook and stir until the vegetables have softened, about 5 minutes.
Stir in spring onions and shiitake mushrooms and continue cooking and stirring for 30 seconds. Pour in the soy sauce mixture then add the noodles. Cook and stir until the noodles are warmed through, 2 to 3 minutes. Remove from heat and toss with sesame seeds and the remaining 1 1/2 teaspoon of sesame oil.