Using a rubber spatula, combine the ingredients for the poolish in a small bowl, scraping the sides of the bowl to bring the mass together. Cover tightly with plastic wrap and refrigerate for 24-72 hours to ferment and develop flavor. the longer the ferment, the deeper the flavor. (SEE NOTE A)
The next day, combine the ingredients for the levain in a pint size glass jar. Cover with a lid but don't screw it on, and place in the warmest area of your kitchen, The warmer the area, the quicker the levain will double in size and become bubbly (active). This will take between 3 to 5 hours, depending on the temperature of the room. (SEE NOTE B)
Once the levain is active, you are ready to make the dough. Combine the bread flour, dark rye flour, caraway seeds, and salt in a large bowl. In a separate bowl, whisk the water, barley malt syrup, and the entire contents of your jar of active levain together until incorporated. Retrieve the poolish from the fridge and whisk it into the levain mixture until incorporated. Add this mixture to the dry ingredients until you have a wet and shaggy looking dough with no traces of dry spots or poolish streaks remaining. Cover the bowl with a kitchen towel and leave it at room temperature for 1 hour.
After the hour, dump the dough onto a floured countertop. The dough will be very sticky so be sure to generously flour your hands and the top of the dough. Press into a 1-inch-thick disk, about 9x9-inches in diameter. Grab an edge of the disk with your hand, stretch it out a few inches and fold it over itself. If the dough is sticking to the counter, add more flour as needed. Repeat this 4 times, rotating the disk 90 degrees each time. Shape the dough into a ball and place it in a container or bowl large enough to allow it to double in size. Cover with a kitchen towel and stack in the warmest part of your kitchen. Again, the warmer the area, the quicker the dough will double in size. We've found that leaving it in an area around 78-80℉, the dough doubled in 2 1/2-3 hours.
When your dough has doubled, spread a clean non-terrycloth kitchen towel inside a large bowl and generously sprinkle with bread flour. Dump the dough onto a floured countertop and repeat the stretching and folding procedure (in step 4) until you have a somewhat smooth ball. Place the ball into the prepared bowl and fold the edges of the towel up and over the dough. Place in the refrigerator overnight (12-24 hours).
The next day place a 7-8 quart Dutch oven with a lid on the middle rack of your oven and crank the heat to 450℉. Leave it there for 2 hours to fully heat the pot. Remove the dough (leaving it in the bowl) from the fridge at this time and place it on a countertop near your oven.
When the 2 hours is almost up, place a 12-inch x 16-inch piece of parchment paper on the countertop. Remove the dough from the towel-lined bowl and place it on the parchment. Brush the top of the dough with some of the egg white and sprinkle the caraway seeds evenly over. Score the top of the dough with a bread lame (if you have one), razor blade, or sharp knife in a criss cross design ar any design you wish. Remove the pot from the oven and take off the lid. Grab the edges of the parchment paper to lift and carefully lower the bread into the hot pot. Cover with the lid and place in the oven for 20 minutes.
Remove the pot from the oven, take off the lid and place back in the oven to bake for another 15 minutes, or until the top is very browned and crackly. Remove the pot from the even and leave the bread in it for 15 minutes before removing it to a wire rack to cool for at least 2 hours. Cutting the bread too soon may result in a gummy center.