Proof the yeast. In a medium sized bowl, whisk together half a cup of water warmed to 110F (46C) with the yeast and one tablespoon of brown sugar. Let rest for 10 minutes until yeast is activated and has poofed.
Make the dough in a stand mixer. In the bowl of a stand mixer with the dough hook attachment, add the proofed yeast mixture with the remaining 1 ¼ cup of warm water with oil, date syrup, and rye flour. Mix for 30 seconds before adding the salt, caraway seeds, and bread flour. Mix on low speed for 4 minutes before increasing speed to medium and mix for another 5 to 6 minutes. The dough will be soft, supple, and slightly tacky when done. Add additional bread flour one tablespoon at a time as needed.
Make the dough by hand. In a large bowl add the proofed yeast mixture with the remaining 1 ¼ cup of warm water with the oil, date syrup, and rye flour. Mix for about 30 seconds with a large wood spoon before adding the salt, caraway seeds, and bread flour. Mix with the spoon for a few minutes before turning the dough out onto the countertop and kneading by hand for up to 10 minutes. The dough will be soft, supple, and slightly tacky when done. Add additional bread flour one tablespoon at a time as needed.
First rise. Place the dough in a lightly greased bowl and cover with plastic wrap or a clean kitchen towel. Let the dough rise in a warm spot for 1 to 2 hours, letting the dough double in size.
Shaping and second rise. Lightly grease a 9x5-inch loaf pan. Turn the dough out onto the countertop and with a rolling pin, roll out to an 8 x 15-inch rectangle. Starting on the shorter 8-inch side, roll the dough tightly so that it will fit into the prepared loaf pan. Cover again and let rise for about an hour or until the dough has risen over the edges of the pan.
Preheat the oven to 375°F/190°C. Make sure the rack is in the middle or lower third of the oven to prevent the bread from burning.
Bake. Bake the bread uncovered for 35 minutes or until the bread reaches an internal temperature of 195°F (46°C). If the bread is browning too quickly, gently tent over a piece of aluminum foil while the bread finishes. Remove the bread from the oven and from the loaf pan to cool on a wire rack for about an hour. Slice, serve, and enjoy!