2 tablespoons vegetable oil (or slightly more, depending on how many batches you divide your dumplings into)
Directions
Peel the ginger and grate it on a fine rasp or microplane.
Grind the Szechuan peppercorns to a fine powder in a spice grinder.
In a mixing bowl, combine ¼ teaspoon of Szechuan peppercorns with the ginger, ground beef, chicken stock, 1 tablespoon of soy sauce, rice wine, and salt. Cover the bowl with plastic wrap and refrigerate.
If making the optional dipping sauce, do so now by stirring together the 2 tablespoons of Chinese black vinegar, 2 tablespoons of soy sauce and 2 teaspoons of sesame oil.
Add the flour to the food processor.
Measure 1 cup of boiling water, and with the processor running, add the boiling water. Process until a dough ball forms (about 30 to 45 seconds).
Lightly dust a work surface with flour and dump the dough onto it, kneading it for 3 minutes.
Form a dough ball, wrap it in plastic wrap, and set it aside to rest for 30 minutes at room temperature.
Trim the ends off the carrot and chop it into 1-inch lengths. Add them to a clean food processor and pulse 10 times.
Trim the stems off the green onions and chop them into 2-inch lengths. Add the green onion and the peas to the food processor and pulse until everything is finely chopped.
Add the processed veggies and 1 teaspoon of sesame oil to the ground beef mixture and mix it well with a spatula.
To make the dumpling wrappers, line 2 rimmed baking sheets with silicone baking mats or parchment paper. Dust lightly with flour and set aside.
Unwrap the rested dough, and cut it into quarters. Cover 3 of the pieces with plastic wrap and set aside.
Take one piece of dough and roll it into a log about 8 inches long. Cut the log in half, then cut each piece in half, and then in half again to get 8 even pieces.
Roll each piece out into a 3- to 3½-inch disc.
Move each disc to the lined baking sheet and cover with plastic wrap to keep them from drying out while you roll the rest of the wrappers. Use a light dusting of flour and a layer of plastic wrap between layers.
Add about 1 tablespoon of the meat filling to each disc, just off-center. Fold the disc into a half-moon, press edges to close, and seal with any method you like.
Move each completed dumpling back to the tray, and cover as you make all the dumplings.
Add 1 tablespoon of the vegetable oil to a non-stick skillet, heating over medium heat until hot.
Add the first batch of dumplings, avoiding crowding, and cook on one side until they easily release from the skillet surface (2 to 3 minutes).
Add 3 tablespoons of water and cover the skillet with a lid. Steam for 3 minutes, at which point dumplings should be cooked through. Repeat for each batch of dumplings.
Serve with optional dipping sauce or another dipping sauce of your choice.