Cook the glass noodles according to package directions until tender, about 6-8 minutes. Drain, rinse briefly with cold water, and toss with 1 tablespoon soy sauce, 1 tablespoon sugar, and 1 tablespoon sesame oil, then set aside.
Blanch the spinach in boiling water for 30 seconds, then drain, squeeze out excess water, and season with a pinch of salt and a few drops of sesame oil, then set aside.
Heat 1 tablespoon vegetable oil in a large skillet over medium-high heat and stir-fry the carrot for 1-2 minutes until just tender-crisp, then remove and set aside.
In the same pan, stir-fry the onion for 2 minutes until softened, then remove and set aside.
Add the mushrooms with the garlic and stir-fry for 2-3 minutes until softened, then remove and set aside.
If using the egg garnish, wipe out the pan, cook the beaten egg into a thin sheet, let cool, and slice into thin strips.
Return the noodles to the pan or a large mixing bowl with the remaining soy sauce and sugar, add all the cooked vegetables, and toss everything together thoroughly, tasting and adjusting seasoning.
Transfer to a serving platter, top with egg strips and sesame seeds, and serve warm or at room temperature.