With a sharp knife, cut both meats into small dices, about 5 mm, (or grind the meat once through the large die of a meat grinder).

Chop the carrots and onions into small dices as well, and mince the garlic. In a pan over medium heat, sauté all the vegetables needed for the filling with half of the olive oil and cook until golden brown. Put aside.

In a pan over high heat, brown the meat in the rest of the olive oil. Reduce the heat to low, add the vegetables, season with the salt and black pepper, and stir for a minute.

Add the stock, cover with a lid, and simmer over low heat for 30 minutes. Let cool, then transfer to a plastic container, and refrigerate for at least 1 hour.

In the bowl of an electric mixer fit with the paddle attachment, place half of the flour, plus the salt, egg, and water. Mix over low speed until homogeneous, scraping down the sides with a spatula.

Add the rest of the flour and mix again until it forms a smooth paste. Keep mixing for one more minute, then wrap in plastic, and let rest at room temperature for 30 minutes.

Divide the dough into four equal parts to proceed in batches. On a floured surface, roll the dough very thinly. You can use a rolling pin or a pasta machine (at the thinnest setting).

Make 9 mm-diameter discs using a cookie cutter or a glass. Place a small spoonful of meat filling at the center of each disc. Holding it in the palm of your hand, shape the disc like a purse, and pinch the edges all around the top. The goal is to create folds on all sides to make the dumpling look pretty, and keep the top of the dumpling closed (it is okay to have a tiny bit of filling showing).

Repeat with the rest of the dough and filling. The dough scraps can be re-rolled to make more dumplings.

Place the dumplings on a steamer lined with parchment paper, and steam in a closed pot for 15 to 20 minutes, depending on the thickness of the dough. If you don't have a "dedicated" steamer, there are plenty of ways to make your own. Search the Internet for inspiration!

Sprinkle the dumplings with finely sliced spring onion, and serve immediately.