Beef marinade: Mix soy sauce, brown sugar, sesame oil and minced garlic. Pour over beef and mix well to coat all slices of the beef. Allow to marinade in the fridge for at least 1 hour.
Mushroom marinade: Fill a saucepan with the dried shitake mushrooms, water, soy sauce and sugar. Heat over medium-high heat till it starts to boil. Turn off the heat, cover the saucepan and let it sit for about 1 hour. When the mushrooms are done marinating, discard the marinade liquid. Cut off the stems and slice the mushrooms into thin strips.
Noodles: Bring a large pot of water to a boil. Boil the noodles for about 7 minutes or until al-dente. Pour into a colandar and thoroughly rinse in cold water. When all of the water has drained, pour sesame oil over the noodles then toss till all of the noodles are coated.
Prepare the sweet soy sauce mixture. Combine soy sauce, brown sugar and sesame oil.
Heat up 2 tablespoons of cooking oil in a wok or large frying pan over medium-high heat.
Stir-fry beef and mushrooms until cooked. Set aside.
Stir-fry carrots and onions until just before the onion turns translucent. Set aside.
Stir-fry minced garlic and spinach until spinach is wilted.
Turn off the heat.
Toss in the noodles as well as the sweet soy sauce mixture. Stir well to combine.
Add the beef, mushrooms, carrots, onions and sesame seeds. Toss to combine all ingredients.
Transfer to a large serving bowl.
Garnish with chopped scallions and sliced red chili.