Keep the beef stew simmering on the stove while you prepare the rest of the ingredients.
Blanch the noodles in boiling water for a minute. Drain. Plunge in iced water and allow to cool. Drain. Divide among six bowls.
Blanch the spinach in boiling water just long enough to wilt. Scoop out and divide into six portions.
Place one portion of spinach in every bowl on one side of the noodles.
Rinse the mung bean sprouts well and drain. Divide into six portions.
Ladle simmering broth directly into the bowls.
Arrange a few pieces of beef on one side of the noodles in the bowl.
Place a portion of mung bean sprouts in every bowl alongside.
Sprinkle in toasted sesame seeds and sliced scallions.
Serve the spicy beef noodle soup at once.