Boil noodles and set aside. Mince garlic and finely dice onions, cut Broccoli into florets, and cut carrots into thin strips. Prepare sauce ingredients in a small bowl.
Blanch the broccoli and carrots. Heat .5 EL in a pan. Add onions, green onions, and blanched broccoli and onions and cook for on medium-high heat for 5 minutes. Start frying noodles now (see instructions below). Reduce heat, cooking vegetables for another 5 minutes on medium-low heat. Finally, add garlic last, along with half of sauce mixture, cooking for about 2 minutes more. Keep warm.
To cook noodles:
Heat 1 TL oil in a pan on medium-low heat. Add sesame seeds and mix with oil. Cook for about 2 minutes. Add noodles and remaining half of sauce, cooking until liquid is gone (about 5 minutes). Remove noodles and arrange in center of a plate. Add vegetables on the edges.