In a large bowl, combine the Bread Flour, Rye Flour, Potato Flakes, Caraway Seeds, Sugar, Yeast, and Salt. Add in the Oil, Pickle Juice, and Water and use a rubber spatula to combine into a wet dough. Cover the bowl in plastic wrap and allow the dough to rest for 30 minutes.
Transfer the dough to a floured counter or mat (do not wash the bowl) and knead for approximately 10 minutes until the dough feels springy and tacky (but not wet). If the dough is feeling very wet, add a bit more Bread Flour gradually and continue kneading. Grease the bowl with cooking spray and transfer the dough back to it. Cover the bowl with plastic wrap and allow the dough to rise in a warm place for one hour. If your kitchen is chilly, try preheating your oven to 200 degrees F, turning it off, and placing your bowl on top of the stove.
Grease a 9 x 5" loaf pan with cooking spray and transfer your risen dough to the pan. Allow to rise again for 40 - 90 minutes, until the dough has risen approximately 1 inch above the top rim. If you'd like to add more caraway seeds as a topping, in a small bowl beat together the egg white and water, and brush on top of the loaf. Sprinkle with caraway seeds.
Preheat oven to 350 degrees and bake for approximately 45 - 55 minutes or until golden brown. Let cool in pan for 20 minutes and then transfer to a cooling rack to cool completely before slicing. Enjoy!