Make the dough: In a large bowl, combine the all-purpose flour and salt. Slowly pour in the warm water, stirring with a fork or chopsticks until a shaggy dough forms.

Knead the dough: Transfer the dough to a lightly floured surface and knead for 8-10 minutes until smooth and elastic. Cover with a damp towel and let rest for at least 30 minutes.

Prepare the filling: In a medium bowl, mix together the cabbage, mushrooms, grated carrot, tofu, green onions, garlic, and ginger.

Add the soy sauce, sesame oil, rice vinegar, white pepper, and cornstarch to the vegetable mixture. Stir well to combine. Taste and adjust seasoning if needed.

Roll out the dough: Divide dough into two equal portions. On a floured surface, roll one portion into a long log about 1-inch thick. Cut into small pieces (about 1 tablespoon each). Roll each piece into a thin circle about 3 inches in diameter.

Fill the jiaozi: Place about 1 tablespoon of filling in the center of each wrapper. Fold the wrapper in half to form a semicircle, then pinch the edges together firmly to seal. You can pleat the edges for a traditional look.

Cook the dumplings: Heat a non-stick skillet over medium heat with 1 tablespoon vegetable oil. Place dumplings flat side down and cook until bottoms are golden, about 2 minutes.

Add ¼ cup water to the skillet, cover immediately with a lid, and steam the dumplings until the water evaporates and dumplings are cooked through, about 5-6 minutes.

Serve: Transfer to a plate and serve warm with the prepared dipping sauce.