In a small bowl, stir together yeast, 1 teaspoon sugar and the water. Allow to stand at room temperature 5 minutes until foamy.
In the bowl of a stand mixer fitted with a dough hook, whisk together flour and salt. Make a well in the center of the flour mixture. Add butter and foamy yeast mixture. Knead for about 5 minutes until smooth. Alternately, this can all be done by hand.
Allow the dough to rest 10 minutes then roll the dough to a 10x14-inch rectangle on a well floured surface. Spread the mustard down the center of the dough, about 3-4 inches wide. Top evenly with corned beef slices. Top the corned beef with sauerkraut then sprinkle the cheese over the top.
Using a sharp knife, make long slits from the filling to the edge of the dough at 1-inch intervals. Repeat on both sides of the filling. Fold the ends of the dough over the filling then starting at the top, fold one long strip over the filling then repeat on the other side. Alternate side to side to form a braid.
Transfer dough to a parchment lined baking sheet. Brush dough with egg wash and sprinkle with caraway seeds. Cover loosely with a clean kitchen towel and allow dough to rise 45 minutes.
Preheat oven to 400°F. Remove the towel and bake bread in preheated oven 25-30 minutes, until golden brown. Cool 10 minutes then serve warm.