Mix together the sourdough starter, flour, salt, butter, and herbs to make a smooth (not sticky), cohesive dough. Divide the dough in half, and shape each half into a small rectangular slab. Cover with plastic wrap, and refrigerate for 30 minutes, or up to a couple of hours, until the dough is firm.
Preheat the oven to 350°F. Working with one piece of dough at a time, very lightly flour a piece of parchment, your rolling pin, and the top of the dough. Place the dough onto the floured parchment and roll it about 1/16" thick. It'll have ragged, uneven edges; that's OK. Just try to make it as even as possible. Transfer the dough and parchment together onto a baking sheet. Lightly brush with oil and then sprinkle the salt over the top of the crackers. Cut the dough into 1 1/4" squares; a rolling pizza wheel works well here. Prick (dock) each cracker a couple of times with a fork; this will help keep them from puffing up like little pitas as they bake. Roll and cut the second piece of dough following the directions above.
When fully browned, remove the crackers from the oven and place the pans on a rack to cool. Store crackers, well wrapped, at room temperature for up to a week; freeze for longer storage.