In a large skillet or wok over medium heat, add oil. When hot, add onion. Cook for 7 minutes, stirring, until onion is lightly browned. Add carrot, broccoli, and bell pepper; stir. Cook for 7 minutes, until vegetables are tender. Add basil; stir until wilted.
Add Annie Chun Organic Udon Noodles, soy sauce, water, vegan fish sauce, sugar, Sriracha, and red pepper flakes; stir. Turn heat to low. Cook for 3 minutes.