Fill a large pot with water and add beef; bring to a boil. Reduce heat and simmer until meat can be punctured with a fork, about 30 minutes. Stir in soy sauce, white sugar, garlic, and ground black pepper; cook and stir until flavors combine, about 15 minutes.
Stir shishito peppers and eggs into the beef mixture. Cook and stir until meat can easily be pulled apart with a fork and liquids have been reduced to a third of the original amount, about 15 minutes.
