Cook the noodles according to the package, but cook for a minute less to avoid a soggy dish. Scoop out some noodle water, for the sauce later, then drain the noodles and set aside.
Whisk together the gochujang, toasted sesame oil, soy sauce, mirin, vinegar, sugar, and gochugaru or red pepper flakes to make the sauce. Set aside.
Heat the avocado oil in a large sauté pan over medium-high heat. Once shimmering, add the scallion whites and greens, garlic, and ginger. Season with a pinch of salt and cook for 1 to 2 minutes over medium-high heat. Add the Napa cabbage and season with a pinch of salt, and stir-fry for 3 minutes, or until it reduces in size and is tender but not soft. You still want the cabbage to have a little crunch. Lastly, add the chopped vegan kimchi, and mix to combine.
Add in the gochujang sauce and the sesame seeds and allow to sizzle. Add in the cooked noodles and use tongs to coat them in the sauce. If it feels dry, add a spoon or two of noodle water to bring the sauce together. Try to add the water a little at a time, you do not want to make the sauce too watery. Cook everything together for 1 to 2 minutes, or until the sauce clings to the noodles.
Turn off the heat, stir in the Thai basil or cilantro and the reserved dark green part of the green onions, a lime wedge, and serve!
This is best served fresh, but you can store the leftovers in an airtight container in the fridge for up to 3 days.