Using an electric mixer fitted with a dough hook, mix together the rye flour, bread flour, yeast, powdered milk, caraway seed, salt and sugar, placing the salt away from the yeast in the mixing bowl.
Squeeze sauerkraut as dry as you can, then chop into small pieces.
Then add the chopped sauerkraut, olive oil, warmed kraut juice, and egg, mixing and kneading with the mixer until the dough is supple, adding a little flour or water (you can use the extra brine from kraut if you need) as needed to achieve the texture.
Place the dough in an oiled bowl and proof, covered in a warm 100F area (I use the proof setting on my Breville oven) for one hour or until doubled.
Turn dough out of bowl and shape into a loaf.
Place in a greased glass 9x5x3 inch loaf pan, covered with oiled plastic wrap, and proof at 100F for 30 minutes more.
Preheat oven to 375F.
Remove plastic from the pan and bake for 25-30 minutes or until golden brown and sounding hollow when tapped.
Brush with melted butter and cool on a wire rack before slicing.