Make dough. Attach a dough hook to your KitchenAid. Add milk, salt, egg, and water to the bowl and mix.
With the kitchen aid running, add the flour one cup at a time. Continue mixing until the flour is smooth and no longer sticks to your hands.
Cover the dough and allow it to rest for 15-30 minutes before using it. (This helps relax the gluten so that it is easier to work with and is more stretchy.
Prepare the meat filling. In a large bowl, combine all the ingredients for the meat filling.
Cover and set aside until you're ready to use it. (If prepping in advance, refrigerate before use.)
Shaping with a mold. To shape with a mold, roll out enough dough to cover the mold. Use a teaspoon to fill each hole with meat.
Roll out another layer of dough and cover the meat.
Using a rolling pin, roll over the top of the mold until the edges protrude, and then gently push the pelmeni out. Repeat with the remaining dough and meat. Use the scraps of dough to make more pelmeni.
Shaping by hand. Divide the dough into three balls. Roll each ball into a thin layer.
Cut the dough into small squares.
Fill each square with a teaspoon of meat and take one into your hand. Fold the dumpling over and press the edges together to seal them tightly. Repeat with the remaining dumplings.
Cook pelmeni. Bring a large pot of water to a boil and season with salt.
Cook for 2-3 minutes or until pelmeni float to the top.
Serve the pelmeni as desired.