In a large mixing bowl, combine the flour, salt, sugar, egg yolk, vanilla extract, and melted butter.
Add the yeast.
Using the dough hook of an electric mixer, knead the dough until it becomes smooth. Slowly add the milk.
Shape the dough into a ball using your hands. Place the dough in a bowl and cover with a clean dishtowel. Put it in a warm spot in your kitchen and let the dough rise for an hour.
Spread flour on your counter or kitchen table and roll the dough into a thick sausage shape.
Cut the dough into 5 pieces and roll each one into a small ball. Let them rest for an additional 15 minutes.
Heat the butter, sugar, and milk in a large pot with a lid on low heat on the stove. This will be the pot for cooking the dumplings.
Using kitchen tongs, place the balls of dough into the pot with a little space between each one. They will rise significantly while cooking. Put the lid on the pot and leave it on. Lifting the lid regularly to check the dumplings could make them deflate.
Steam the dumplings on medium heat for about 5-6 minutes, then turn the heat down to low and steam them for 18-22 minutes more.
The milk will have completely evaporated when you no longer see bubbles forming on the bottom of the pan, and you will see less steam on the lid. You will also hear a sizzling sound.
Turn off the heat. Leave the lid on for another minute to let the dumplings get just browned on the bottom.
Carefully lift the lid off the dumplings and use kitchen tongs to gently lift the dumplings out of the pot.
Let the dumplings rest on a plate for another minute more and serve.