In a large mixing bowl, combine the ground beef, green onions, garlic, soy sauce, sesame oil, salt, and black pepper. Mix well until all ingredients are fully incorporated.
Take a dumpling wrapper and place about 1 tablespoon of the beef mixture in the center. Moisten the edges with water, fold the wrapper in half, and pinch to seal. Repeat with the remaining wrappers and filling.
In a large pot, heat the vegetable oil over medium heat. Add the sliced mushrooms and sauté for about 3-4 minutes until softened.
Pour in the beef broth and bring to a simmer. Carefully add the dumplings to the pot and cook for about 5-7 minutes, or until they float to the top and are cooked through.
In a small bowl, whisk the eggs. Slowly drizzle the eggs into the simmering soup, stirring gently to create egg ribbons.
Add the baby spinach and gochugaru (if using) to the pot. Cook for an additional 1-2 minutes until the spinach is wilted.
Taste the soup and adjust seasoning if necessary. Serve hot, garnished with chopped cilantro.