In a large bowl, add flour and make a well in the center. Pour in 1/4 cup of the warm milk and sprinkle with yeast and sugar. Gently stir the yeast into the milk and a small amount of the flour. Cover and let rest for 20 minutes, until the yeast becomes frothy.
Pour in the remaining milk, egg, and 1/2 teaspoon salt. Mix together with your hands and knead until smooth. Divide the dough into 8 equal pieces. Roll each piece into a ball and place on a lightly floured surface. Cover and let rest for 40 minutes.
In a wide pot or large, deep skillet, combine water and remaining salt. Bring to a boil and add the butter. Once melted, arrange the dough in the pot with 1-2 inches between each ball. Cover with a tight lid and reduce heat to low. Simmer for 20 minutes without removing the lid. Remove lid once all liquid has evaporated and dumplings have a crust on the bottom (there will be a crackling sound). Remove pot from heat and gently take out dumplings.
Serve hot with vanilla sauce and powdered sugar.