Place the sourdough starter in a medium-sized non-reactive bowl that has a lid. Stir in salt, caraway seeds, onion powder, and fat of choice until thoroughly blended.
Add rye flour to the starter mixture. Use your hands to mix it in well. Knead the dough briefly right in the bowl; cover and let proof at room temperature about 8 hours or overnight.
When ready to bake, divide the dough in 2 pieces. Roll out each piece of dough on a piece of parchment paper or an 11½ x 16½-inch silicon baking mat. Be sure the dough is rolled as thin as possible.
Score the dough in 2-inch squares, using a rolling pizza cutter or a sharp knife. Prick each square with the tines of a fork to keep the dough from puffing up as it bakes. Sprinkle the dough with additional sea salt, pressing it lightly into the dough with the palm of your hand.
Slide the silicon mat or parchment paper onto a baking sheet. Bake in a preheated 350°F (325°F for convection) for about 15 minutes, checking frequently after 10 minutes to make sure crackers are not getting too brown. You may need to remove the outer rows of crackers before the center rows are fully baked, as the entire tray of dough does not always bake evenly. Crackers should feel thoroughly dry to the touch. They will continue to crisp up as they cool.
Cool on a rack, separating any crackers that did not already break apart at the score lines. Store in an air-tight container at room temperature for a week or freeze for longer storage.