1 1/2 tsp. active dry yeast
4 tbsp. sugar, divided
1/4 c. lukewarm water (110°F)
3/4 c. lukewarm milk (110°F)
4 tbsp. melted butter, divided
1/4 tsp. salt
2 1/2 c. sifted all purpose flour, or more if necessary
1/2 c. cold milk
Dissolve yeast and 1 tablespoon sugar in the warm water. Let stand 5 minutes, or until bubbly.
In a bowl, stir the milk, melted butter, 1 tablespoon sugar, and 1/4 teaspoon salt until dissolved. Add the bubbling yeast mixture and then the flour, beating until a smooth dough forms. Add flour as necessary, until the dough can be formed into a soft ball.
Turn dough out onto a lightly floured board and knead for 5 minutes. Place it back in the bowl, which has been lightly greased or sprayed. Let rise in a warm place until doubled, about 45 minutes.
Punch dough down, divide into 12 pieces, shape the pieces into balls. Place the balls 2 inches apart on a lightly oiled baking sheet, cover with a clean towel and let rise in a warm spot until doubled, about 45 minutes.
Melt 2 tablespoons butter in a 10 inch skillet or saucepan with a tight lid. Stir in 2 tablespoons of sugar and the milk and bring to a boil. Reduce heat to low, arrange the dumplings in the saucepan and cover. Simmer for 25 minutes without peeking and then check. Keep simmering until the dumplings have absorbed all the liquid. Remove from heat but keep warm until serving.
Vanillesoße
4 egg yolks, lightly beaten
1/2 cup sugar
2 cups milk
1 tsp. vanilla extract
Beat the egg yolks and sugar together until the yolks are thick and pale yellow and the sugar is dissolved, about 4 minutes.
Bring the 2 cups of milk to a boil in a heavy 2-quart saucepan and then pour over the egg yolks in a thin stream, using a whisk or electric mixer to stir constantly. Pour back into pan and heat without boiling until mixture coats the back of a spoon. Remove pan from heat and stir in vanilla extract.
Serve the Dampfnudeln on a dish bottom side up and pour the vanilla sauce over. Savor this sweet and unusual dessert, because this is the first and last time you will ever make it!