Activate yeast: Stir the yeast and sugar into 125 ml lukewarm milk. Let sit 5 minutes until foamy.
Mix: Add the flour and salt to a stand mixer bowl. Add the melted butter, eggs, and yeast milk. Mix on low with the dough hook, adding more milk as needed for a soft dough.
Knead: Knead 6 to 8 minutes until smooth and the dough pulls away from the bowl.
First rise: Cover and let rise in a warm spot for about 1 hour, until doubled.
Shape: Knead briefly, divide into 10 to 12 pieces, and shape into smooth balls.
Second rise: Cover and let rise 20 to 30 minutes, until puffy.
Prepare the pan: The dumplings won’t fit in one pan, so use two pans or cook in two batches. For each, heat the milk, butter, sugar, vanilla sugar, and salt in a pot with a tight-fitting lid until the butter melts and the milk begins to simmer.
Add dumplings: Place half the dough balls in each pan (or the first half for batch one), leaving a little room between them. Keep the remaining dough balls covered.
Steam: Cover tightly, reduce heat to low, and cook about 25 minutes. Do not lift the lid.
Check: When you hear crackling and smell caramel, the liquid is gone and the bottoms are golden.
Serve: Remove from the pan and serve warm, caramelized side up, with vanilla sauce if desired.