In a mixing bowl, combine shredded cabbage, shredded carrots, chopped shiitake mushrooms, chopped scallions, minced garlic, minced ginger, soy sauce, sesame oil, sugar, salt, black pepper, and mashed tofu. Mix well to combine.

In another mixing bowl, combine all-purpose flour, warm water, and salt. Knead the dough until smooth and elastic.

Roll the dough into a log and cut into 24 equal pieces.

Roll each piece into a small circle with a rolling pin, or use a dumpling press to make the process faster.

Place a spoonful of filling in the center of each circle and fold the circle in half, pinching the edges to seal the gyoza.

Heat a frying pan over medium-high heat and add a small amount of oil.

Place the gyoza in the pan and fry for 2-3 minutes until the bottoms are golden brown.

Add 1/4 cup of water to the pan and cover with a lid. Steam the gyoza for 5-7 minutes until the filling is cooked and the wrappers are translucent.

Remove the lid and continue cooking until the water has evaporated and the bottoms are crispy.

In a small bowl, mix together soy sauce, rice vinegar, sesame oil, and sugar to make a dipping sauce.

Serve hot.