Make the omelet: beat the egg, add in a pinch of salt. Heat a small pan over medium heat. Add oil, swirl to coat. Turn to low and pour in the egg. Swirl the pan gently so that the egg spreads evenly. Cook on low for a minute or two. Flip the egg over, turn off the heat and the other side cook for another minute. Transfer the egg to a cutting board and let cool. Slice into thin strips. Set aside.
Prepare the spinach: blanch the spinach in boiling water for 15-seconds. Remove, squeeze to drain liquid. Toss the spinach with a teaspoon each of soy sauce and sesame oil. Set aside.
Cook the noodles: cook the dangmyeon noodles in a boiling water for 8 minutes. Stir ever two minutes to make sure they don't stick. Strain the noodles. Cut them twice with scissors (otherwise the noodles will be too long). In a big mixing bowl, mix/toss the noodles with two teaspoons each of sesame oil and soy sauce. Add in the spinach, toss to mix. Set aside.
Cook the vegetables: heat skillet to medium-high. Add oil, and stir fry the sweet onion and green onion together for two minutes (till sweet onions just start to turn translucent). Add it to the big mixing bowl with the noodles.
Wipe the skillet. Stir fry the shiitake mushrooms for one minute. Season with a bit of salt. Add it to the big mixing bowl.
Wipe the skillet. Stir fry the carrots for three minutes. Season with a bit of salt. Add it to the big mixing bowl.
Wipe the skillet. Stir fry the red bell peppers for two minutes. Season with a bit of salt. Add it to the big mixing bowl.
Now all the vegetables and noodles are together in one big bowl. Give it a good mix.
Make the "sauce." In a small bowl, combine: 8 minced garlic cloves, 2 tablespoon soy sauce, 1 tablespoon honey, and 1 tablespoon sesame oil. Mix the sauce well, and pour the sauce over the bowl with the noodles. Mix again till evenly incorporated.
Add the sliced egg and 2 tablespoons toasted sesame seeds. Mix gently once more and serve! Wonderful hot but also great at room temperature. Leftovers heat up well in the microwave.