Whisk the soy sauce, rice vinegar, ketchup, cane sugar, vegan oyster sauce, and black pepper together in a small bowl until the sugar is dissolved. Taste the mixture and add a bit more sugar if you prefer a sweeter sauce.

Rinse the noodles under warm running water to help them separate without breaking, then drain them well to prevent the stir-fry from becoming watery.

Heat the oil in a large skillet or wok over medium-high heat until it shimmers but does not smoke. Add the scallions and onion and sauté until they are fragrant and the onion becomes slightly translucent, about 2 minutes.

Add the carrot, cabbage, bell pepper, mushrooms, and salt. Increase the heat to high and stir-fry for 3 to 4 minutes—the vegetables should be tender on the inside but still have a distinct snap on the outside.

Add the noodles and the sauce to the pan. Toss everything together well and cook for another 2 to 3 minutes until the noodles are fully coated and the sauce has been mostly absorbed.

Transfer the noodles to plates and top with extra scallions and a sprinkle of togarashi. Serve hot while the vegetables are still vibrant.