Bring a large pot of water to a rolling boil. Add the udon noodles and stir gently to prevent sticking. Cook for 8-10 minutes until just tender and chewy. Drain and rinse under cold water to stop the cooking and set aside.
In a small bowl, whisk together soy sauce, miso paste, sesame oil, minced garlic, and grated ginger until smooth. Set this flavorful sauce aside.
Heat the vegetable oil in your wok or skillet over high heat until shimmering and hot. Add the mixed vegetables and stir-fry for about 3-4 minutes until fragrant and slightly tender, listening for a gentle sizzle.
Add the drained udon noodles to the wok with the vegetables. Toss gently to combine the ingredients evenly, allowing the noodles to heat through and absorb the flavors.
Pour the prepared sauce over the noodles and vegetables. Toss vigorously with tongs or chopsticks for 2-3 minutes until the noodles glisten with sauce and develop a slight sticky coating. You should hear a gentle sizzling as the sauce thickens.
Taste the dish and adjust seasoning if needed—perhaps a splash more soy or sesame oil. Continue tossing for another minute to let flavors meld and the noodles become perfectly chewy and glossy.
Remove the wok from heat, garnish with chopped scallions if desired, and serve immediately while hot and fragrant. Enjoy the satisfying chewiness and umami-rich flavors in every bite!