In a spice grinder or blender, pulse the sunflower and pumpkin seeds until they form a fine powder. Pulse judiciously: you want a powder, not a nut butter. Transfer the powder to the bowl of a stand mixer or a mixing bowl. Then pulse the flaxseeds until they too form a fine powder and transfer it to the same bowl. Combine these with the flours, the whole sesame seeds, salt, oil, honey, and water. If using a stand mixer, mix it all with the paddle attachment on a slow speed for 1 to 2 minutes. If mixing by hand, stir with a large spoon for 1 to 2 minutes. It should form a firm, unsticky ball. (If not, add flour or water as needed.) Then transfer the dough to a floured surface and knead very briefly to make sure the dough holds together and the ingredients are distributed throughout the dough. The dough will feel very slightly tacky but not sticky.
Heat the oven to 300° F. For every pan of crackers that you want to make now -- well-wrapped, the dough will hold for a week in the fridge and up to three months in the freezer -- line a baking sheet with parchment paper.
Divide the dough into four equal pieces. Working on a well-floured surface and using a rolling pin, roll the dough out until it is relatively thin (Reinhart suggests 1/16 of an inch). The dough may stick in the process, so check it frequently, lifting it up to see if it needs more flour or flipping the whole thing over. If the dough pulls back instead of obediently rolling out, let it rest for a few minutes and then begin again.
Separate the egg and whisk the white with 2 tablespoons of water. (Save the yolk for something else.) Then paint the dough's surface with the egg wash and sprinkle it with sesame seeds and poppy seeds. Using a pizza cutter or a metal dough scraper, cut the dough into your preferred cracker size and shape. Then gently transfer the shapes to the prepared baking sheet. (Reinhart notes that because the crackers won't spread or rise, they can almost touch.)
If you are making multiple pans, you can bake them all at the same time. (Bake for ten minutes and then rotate the pans; bake for another ten and rotate again.) After approximately 25 or 30 minutes, depending on how thin you rolled the dough, the crackers should be about done, which means bordering on golden brown, well-dried, and crisp. (If the crackers are still pale, increase the heat to 325 once they begin to crisp.) Leave the crackers on the baking sheet so they crisp up more. They should snap when cool. (If they don't, return them to the oven for a few more minutes.)
Let the crackers cool for at least 15 minutes. They will keep in an airtight container on the counter for a week (or in the freezer for far longer).