1.In a pot, bring the chicken broth and water to a boil. Once boiling, cover, and lower the heat to keep it simmering.
2.Meanwhile, place a pan over medium-high heat until hot. Once hot, add the oil to coat the bottom of the pan. Crack the eggs into the pan, and cook over medium-high heat until the eggs are browned around the edges.
3.Flip the eggs over and do the same to the other side, making sure the eggs are cooked through completely. Transfer the fried eggs onto a plate and cut into bite-size pieces with scissors.
4.Add egg to simmering soup. Increase the heat to high, and add tofu and mushrooms. Cover and boil for 10 minutes over high heat.
5.Next, add the napa cabbage. Cover and cook for another 5-10 minutes, or until the cabbage is very tender. Add the sesame oil, salt to taste, and white pepper. Top with cilantro and green onion and serve.