In a small bowl, mix together the gochugaru, soy sauce, garlic, and salt until it forms a paste. Add the beef and mix until the beef is completely coated.
Heat a medium-sized saucepan over medium-high heat. Add a tablespoon of oil. Add the beef and saute until browned. Add the water or broth, turn the heat to high, and bring to a boil. Add zucchini, jalapeno, shiitake, and scoop in the tofu. Try to keep the tofu intact in large chunks. Bring the mixture to a boil again. Lower the heat to medium and let simmer for about 20 minutes.
Before serving, stir in the sesame oil and green onions. Ladle the soup into individual bowls and serve immediately.
Egg option: Ladle the soup into individual bowls while piping hot. Crack an egg into each bowl and serve immediately so the individual can fold the egg into the hot soup to cook it.