To begin, combine the rye flour, oil, molasses, salt, yeast, caraway seeds, water, and 2 cups of the bread flour in the bowl of your stand mixer. Turn on your mixer (fitted with the dough hook) and while it mixes, gradually add in the remaining 2 cups of bread flour. Let the mixer run for 6 minutes. Take the dough out, form it into a ball, and then place it in a lightly oiled bowl. Turn the dough to coat the top with oil.
Cover the bowl with a tea towel and place it in a warm location to rise for an hour. Not sure where to let the dough rise? Turn the light on inside your oven and set the bowl inside. The bulb puts off enough heat to create a very happy place for the dough to rise in a draft-free location.
An hour later, the dough should have doubled in size. On a lightly floured surface, turn the dough out and cut it in half. Pat the dough out into a rectangle that is about 7×14 inches. Starting on a long side, roll the dough tightly into a log. Place the loaves on a baking stone or sheet tucking the ends underneath. I am using a well-seasoned stone. If using a cookie sheet or unseasoned stone, line it with parchment paper or lightly grease it first. Cover with the tea towel again and place it back in its warm location to rise again.
After about 30 minutes, if you touch the dough, a light indentation should remain. Set your sheet out on the counter and begin heating your oven to 400 degrees. With a sharp knife, slash the tops of the loaves 3 or 4 times at an angle.
In a small dish, beat an egg white until frothy. Brush the egg white over the loaves. When your oven is fully heated, bake the bread for 30-35 minutes or until they sound hollow when tapped.