Boil noodles in lightly salted water until al dente, veering on the side of undercooked (you will be stir-frying them later, so avoid overcooking them now). Drain and rinse with cold water to prevent sticking. Set aside.
Heat a wok or large frying pan over medium-high heat. Add oil and swirl around, then stir-fry the garlic, ginger, and shallot/onion 1 minute.
Add the short ribs in shredded large chunks, the carrots, plus 1 to 2 tablespoons of the noodle sauce you made earlier--enough to keep the ingredients frying nicely. Stir-fry 2 minutes, until carrots soften slightly.
Add the mushrooms, broccoli, and red pepper, plus 3 to 4 more tablespoons of the short rib sauce. Continue stir-frying until mushrooms and red pepper soften and broccoli turns bright green but is still crisp (3 to 4 minutes).
Now add the noodles plus remaining sauce. Using two utensils, lift and turn the noodles in the pan to combine with the vegetables. Stir-fry in this way 3 to 5 more minutes, or until you are happy with the softness/texture of the noodles. During the last 1 minute of cooking time, fold in the bean sprouts.
Serve immediately in bowls or on plates, topping with a sprinkling of fresh coriander or basil. More fresh bean sprouts can also be added as a topping.