In a small bowl, combine warm milk (about 110°F/43°C), sugar, and yeast. Let sit 5–10 minutes until foamy.
In a large bowl or stand mixer, combine flour and salt. Add the yeast mixture, melted butter, and egg. Mix and knead (by hand ~8 minutes, or stand mixer with dough hook ~5 minutes) until smooth and elastic.
Place dough in a greased bowl, cover, and let rise in a warm spot until doubled, about 1 hour.
Slice the sausage ring or links into 8 even portions, about 10–12 cm each.
Punch down the risen dough and divide into 8 equal pieces. Roll each piece into an oval about 15 cm x 10 cm.
Spread about 1 tsp mustard down the center of each dough oval, then top with about 1 tbsp sauerkraut and a sausage portion.
Fold the dough up and around the filling, pinching the seams to seal completely. Place seam-side down on a parchment-lined baking sheet.
Cover loosely and let rest 15–20 minutes while preheating the oven to 375°F (190°C).
Brush the tops with beaten egg wash.
Bake 18–22 minutes, until golden brown. Cool slightly before serving.
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