Make the caraway tea. Heat water in an electric kettle or on the stove until it reaches a low simmer (160°F). Pour 300 grams water over the caraway seeds and let steep in the fridge 8-10 minutes until lukewarm to the touch (90°-110°F).
Combine dry ingredients. In the bowl of a stand mixer fitted with a dough hook, combine bread flour, rye flour, salt, sugar, and yeast. Make sure the yeast and salt are not touching in the bowl.
Add the caraway tea. With the mixer running on low, slowly pour the caraway tea and caraway seeds into the center of the dry ingredients. Increase the speed to low-medium, pausing occasionally to push the dry ingredients into the center of the bowl with a spatula. If the dough hasn't come together with no dry bits left in the bottom of the bowl after 3 minutes, sprinkle additional ½ tablespoon of water onto the dry bits and let the mixer run for another 30-45 seconds. Repeat again only if needed.
Knead. Once the dough has mostly come together on the dough hook with minimal dry flour in the bottom of the bowl increase the speed to medium and knead for 3 minutes until the dough clears the sides of the bowl and is smooth and slightly tacky to the touch.
Rise. Shape the dough into a ball and place in a lightly greased bowl. Cover and let rise 1 hour until just about doubled in size. When you press a finger into the dough the indentation should fill back in just slightly.
Punch down. Punch the dough down in the bowl to knock any large air bubbles out of it. Cover and let rest an additional 10 minutes.
Divide and shape. Use a kitchen scale to divide the dough into 8 equal pieces. On a clean, unfloured counter, shape each one into a ball: Stack any smaller pieces on top of the biggest piece. Gently flatten the dough, then tucking the edges up, flip the dough over and cup your hand around it in a claw shape. Keep your pinkie on the counter and move in tight circular motions to build tension on the top of the dough and smoosh the edges together underneath. If that doesn't work for you: Cup your hand around the dough and, with your pinkie on the counter, pull your hand straight toward your body. The dough will tighten up into an oval shape. Rotate 90° and repeat to pull the oval into a circle shape. Rest. Cover the dough balls and let them rest 10-15 minutes. Rye flour is low in gluten so needs a bit of time for the seams on the bottom to close up. Depending on the temperature and humidity in your kitchen, you may need to let them rest an additional 5-10 minutes here.
Preheat the oven and water bath. While the bagels rest, preheat oven to 425°F. Fill a wide, straight-sided skillet with about 3" of water and bring to a low boil. Line a sheet pan with a silicone mat or parchment paper.
Poke the holes. Dust your hands lightly with flour (regular AP or bread flour is fine). Poke your thumb through the bottom of each bagel round, pushing any edges or seams into the center. Gently squeeze to stretch (don't tear!) the bagels — you want the hole to be about the same width as the sides of the bagel. Rotate the bagels through your hands, squeezing to slowly stretch them.The bagels will shrink slightly when they boil and bake, so if you prefer a bigger hole just stretch them a bit bigger.
Rest. Cover the bagels with a damp paper towel and let rest for 10 minutes.
Boil and bake. Working in batches, boil the bagels 1 minute and 30 seconds per side. Use a wire spider to remove the boiled bagels to the prepared sheet pan. Brush with egg wash and bake 20-22 minutes until lightly browned on top.
Cool. Let bagels cool on the sheet pan 5 minutes, then remove to a wire rack to finish cooling completely.