In a large mixer bowl, combine 4 oz active sourdough starter, 6 oz warm water, 1 ½ teaspoons table salt and 1 ½ oz honey. Add 5 oz bread flour and mix to form a smooth batter. If using a stand mixer, switch to the dough hook and add 5 oz rye flour all at once and mix until the dough gathers on the hook. If mixing by hand add as much of the flour as you can with a spoon or spatula, then turn out onto a floured work surface and finish adding the flour by hand.
Turn the dough out onto a floured surface and knead until the dough comes together. Set the dough into a lightly oiled bowl, turning once to coat the dough, cover and allow it to sit at room temperature for 3-4 hours. Every hour turn the dough out and knead 1-2x, return to the bowl and cover again. At this point you can refrigerate the dough overnight and finish the next day
Preheat the oven to 400 °F. (If you have a baking stone preheat it to 450 °F for at least an hour). Line up to 4 half sheet pans with parchment paper (see note 2).
Divide the dough into 16 pieces. Shape each piece into a ball and let rest 4 to 5 minutes on a floured surface. Flatten each ball into a disc. If you have a pasta roller use that to roll the dough (I rolled to #5 thickness).
If rolling by hand roll each dough portion to 1/16" thick, the thinner the dough the crisper the bread. Sprinkle the crackers with caraway seeds and pat them into the surface.
Place the dough rounds onto the parchment lined baking sheets or is you're using a baking stone you can bake the breads in batches, as many as can fit on the stone at a time.
Bake about 5 10 minutes until golden brown and crisp. They'll bake faster on the baking stone than on a sheet pan.
Notes
If measuring the flour by volume use the “dip & sweep” method. That is, dip the measuring cup into the flour bin, overfill it, then sweep away the excess.