Add all of the ingredients to the bowl of a food processor, with only 1 tablespoon of water. Pulse until tiny crumbs form. Add more water, 1 tablespoon at a time, to bring the dough together if needed. Flatten the dough into a disc, cover with plastic wrap (or a reusable wrap of your choice), and chill for 30 minutes and up to 2 days. Note: you can make the dough by hand too, with a pastry cutter if you have one.

Preheat your oven to 325 F. Line a baking sheet with parchment paper.

Divide the dough in half. With a rolling pin, roll the dough out as thin as possible, about ⅛-inch thick. Do this on parchment paper to prevent sticking.

Cut the dough using a 1 ½-inch mini cookie cutter. Alternatively, use a sharp knife. Place onto the lined baking sheet spaced one finger-width apart. Dock the center with a toothpick or the tip of a skinny toothbrush, or leave undocked if you prefer. Chill for 5-10 minutes before baking. Gather the scarps, re-roll and shape again.

Bake the sourdough crackers on the center rack until puffed and light golden brown, about 15-18 minutes or more, depending on thickness. Cool directly on the sheet pan; they will continue to crisp as they cool. If the crackers are slightly soft in the center due to the thickness of the dough, return to a low oven set to 250 F and bake until crisp.

Sprinkle with extra thyme leaves to serve.

Once completely cool, store the crackers in an air-tight container for up to 3 days.