Begin by prepping all of the necessary ingredients.
Either soak the udon if using fresh, or boil and drain dry udon noodles. Set aside.
Slice the carrot into matchsticks or julienne slices about about 2-inches long.
Finely mince the garlic, grate the ginger, and slice the onion longways, thinly.
Slice the bell pepper into long, thin strips.
Cut broccoli into small, bite-sized florets.
Finely shred the cabbage.
In a mixing bowl or large glass measuring cup, add soy sauce, toasted sesame oil, rice vinegar, sugar, vegan mushroom oyster sauce*, grated ginger, and ketchup.
Whisk together until the sugar is dissolved.
Heat a large pan or wok with a high-heat neutral oil like canola.
Once hot, add sliced onions with a pinch of salt and sauté until soft.
Add bell pepper, carrots, mushrooms, broccoli, and minced garlic.
Sauté again on high heat for about 1 minute.
Add shredded cabbage and ½ cup of water to allow the carrots and cabbage to soften.
Once all the water has evaporated, remove about ½ of the vegetables and set aside in a bowl. Drizzle the set aside vegetables with 1 tablespoon soy sauce.
Once the vegetables still in the pan are cooked, soft, and lightly browned, add the soaked/boiled and drained udon noodles.
Pour in the sauce and carefully toss/sauté until the noodles are heated through and the sauce is absorbed.
Add the separate bowl of vegetables back into the pan and toss everything together, careful not to break the udon noodles.
Separate into two bowls for serving, garnish with sliced scallions and sesame seeds.