In a large bowl, whisk the yeast with the water and let stand until foamy, 10 minutes. Add 2 1⁄2 cups of the whole-wheat flour and stir until smooth. Cover the dough with plastic wrap and let stand for 30 minutes.
Uncover the dough and, using your hand, stir the salt and oil into the dough and then add the remaining 2 1⁄2 cups whole-wheat flour and mix until the dough comes together. Scrape the dough onto a lightly floured work surface and knead until smooth and elastic, about 10 minutes. Place the dough in a large bowl greased with oil and cover with plastic wrap. Let stand until doubled in size, about 1 1⁄2 hours.
Place a baking stone on a rack in the oven and heat the oven to 500° for 30 minutes. Meanwhile, punch the dough down and divide into 16 equal pieces. Roll each piece into a ball and then flatten into a 5-inch circle. Lightly sprinkle the cracked wheat bran, if using, or more whole-wheat flour over 2 parchment paper-lined baking sheets. Divide the dough circles between the baking sheets and loosely cover with a kitchen towel. Let stand until slightly puffed, about 30 minutes.
Working in batches, place the dough circles on the hot baking stone, spaced 2 inches apart, and bake until puffed and lightly charred in spots, 6 to 8 minutes. Transfer the breads to a rack and let cool for 5 minutes before serving.