Measure all ingredients and prepare a large wok or wide frying pan. Bring a sufficiently large pot of water to a boil for the mie noodles. Peel the carrots, halve them lengthwise and cut them into thin sticks. Halve the bell pepper and remove the stem, seeds and white membranes. Wash the bell pepper and cut it into thin strips. Wash the broccoli and divide it into small, evenly sized florets. Peel the broccoli stalk and cut the tender inner part into thin slices.

Clean the mushrooms with a cloth or brush and cut them into slices. Trim and wash the spring onions, then slice them diagonally into fine rings. Set aside some of the green spring onion rings for garnish. Peel the garlic and ginger and chop both very finely. Wash and halve the chili lengthwise and remove the seeds for a milder dish. Then cut the chili into very fine rings.

For the sauce, mix the soy sauce, sweet chili sauce, hoisin sauce and sesame oil in a small bowl. Cut the lime in half and squeeze out the juice. Add the lime juice and brown sugar to the sauce and stir until the sugar has mostly dissolved.

Cook the mie noodles according to the package instructions, checking them about one minute before the stated time. The noodles should remain slightly firm because they will continue cooking in the wok. Drain the noodles in a sieve, rinse them briefly with cold water and allow them to drain thoroughly. Toss the noodles with a small amount of the prepared sauce to prevent them from sticking together.

Toast the sesame seeds briefly in a dry pan without oil until fragrant. Remove the toasted sesame seeds from the pan and set them aside.

Heat the wok or large frying pan over high heat and add the vegetable oil. Add the carrots and broccoli to the hot wok and stir-fry for about three minutes. Add the bell pepper strips and mushrooms and stir-fry vigorously for another three to four minutes. Add the garlic, ginger, chili and the white parts of the spring onions. Stir-fry everything for about one minute until the garlic and ginger are fragrant.

Add the drained mie noodles to the vegetables in the wok. Thoroughly toss the noodles and vegetables together using two spatulas or tongs. Pour the prepared sauce evenly over the noodles. Continue stir-frying everything over high heat for two to three minutes, tossing regularly. Make sure the sauce coats the noodles evenly without burning on the bottom of the wok.

Taste the Asian-style noodles and adjust with additional soy sauce, lime juice, pepper or chili if needed. Use additional salt carefully because soy sauce and hoisin sauce are already salty. Roughly chop the peanuts if using them. Divide the finished noodles among bowls or deep plates. Sprinkle with the toasted sesame seeds, reserved green spring onion rings and optional chopped peanuts. Serve the Asian-style noodles immediately while hot.