In a large bowl, combine ground beef, shredded Napa cabbage, chopped green onions, minced garlic, grated ginger, soy sauce, sesame oil, white pepper, and salt. Mix thoroughly and let sit for 15 minutes.
Place about 1 teaspoon of filling in the center of each gyoza wrapper. Wet the edges with water, fold in half to seal, and press firmly.
Heat oil in a skillet over medium-high heat. Cook gyoza for 3-4 minutes on each side until golden brown. Add water to steam for a few minutes.
In a pot, combine chicken broth, water, soy sauce, rice vinegar, sesame oil, grated ginger, and black pepper. Bring to a simmer.
Add cooked gyoza to the broth and let them mingle for 5 minutes before serving.