Stir yeast and brown sugar into warm water, allow to stand for 10 minutes – it should get very bubbly.
In a large mixing bowl, combine flours, caraway seeds and salt. Pour in yeast mixture, stir well to combine. Dump dough out onto a floured surface, knead until soft and elastic, 5-10 minutes.(OR: mix it in a stand mixer with a dough hook for 5 minutes or so!)
Once dough is fully kneaded, place in a greased bowl, cover with plastic wrap, and allow to rise in a warm place for one hour, or until doubled in size.
Once dough has doubled in size, roll out on a floured surface. Aim to make it a large rectangle, say 15 x 20″ or so.
Scatter half of the cheese across the rolled dough, avoiding the very edge of the rectangle. Evenly layer corned beef over cheese, again avoiding the very edge. Scatter drained sauerkraut over meat, top with remaining cheese.
Starting with one of the shorter edges, tightly roll the dough up. Generously grease or spray a 9 x 13″ baking pan.
Using a very sharp knife, slice the roll into 6 even rounds. Carefully place each roll into the pan, spacing them evenly.
Cover pan with plastic wrap, allow to rise one more time – about an hour. While waiting for the buns to rise, heat oven to 375F.
Once final rise is over, pop the pan in the oven and bake for 35-40 minutes, or until golden brown and perfect.
Allow to cool for a few minutes, if you’re patient. Serve hot, preferably with a drizzle of Thousand Island or Russian dressing! (Hey, the whole idea was themed around cinnamon buns, may as well continue that thought in serving them!)