Preheat oven to 450° F. Place a large baking sheet in the oven to heat.
Combine the flour, baking powder, salt, herbs, and yeast in a large bowl. Whisk until distributed.
Using the back of a wooden spoon (or with your fingers), make a well in the center of the dry ingredients.
Add the olive oil and the cool water and stir just until the dough comes together. It should pull away from the sides of the bowl and begin taking a ball form.
Place the dough on to a clean and dry flat work surface.
Using the palms of your hands, knead 5-7 times until dough is smooth. There should be no pale streaks left. Keep in mind, at this point, the dough will still be fairly oily, that's okay. Do not add any more flour.
Using a sharp knife or pastry cutter, divide the dough into 4 equal portions.
Working with one of the portions, place the dough between two sheets of parchment paper. Using a rolling pin, roll the dough out until it's a very thin layer of dough, less than ⅛ inch. The sheet should be about 14x8 inches in diameter.
Remove the top sheet of baking parchment. With a knife or a pizza cutter, lightly score the sheet. This helps make them easier to break into pieces once they are baked. Just don't cut all the way through.
Sprinkle the dough sheet with a little fine ground sea salt, or your favorite salt.
Transfer the prepared sheet of dough into the oven to bake on the heated baking sheet.
Bake for 6-7 minutes until the thinnest parts are golden brown. Remove from oven and allow to cool completely (leaving the baking sheet in for the next batches).
Repeat with the remaining three portions of the cracker dough.
Once they have completely cooled, break them along the scored lines.