In a large mixing bowl, combine the yeast, brown sugar, and plant-based milk or water. Stir until the yeast and sugar are dissolved. Let stand for 7-8 minutes, until the mixture is foamy and active looking.

Add the semolina flour, bread flour, salt, and olive oil. Stir until a shaggy dough forms, then knead by hand or with a stand mixer fitted with a dough hook for 8-10 minutes, until the dough is smooth, soft, and slightly tacky.

Transfer the dough to a lightly oiled bowl, cover, and let rise in a warm place until doubled in size, 60 to 90 minutes.

Turn the dough onto a lightly floured surface and divide it into 8 equal portions. Shape each portion into a ball, cover with a clean kitchen towel, and let rest for 20 minutes.

Roll each dough ball into a circle ¼ inch (6 mm) thick.

Heat a large dry cast-iron skillet or heavy skillet over medium heat. Cook 1 round at a time. After 2 minutes, when bubbles have formed and the underside is golden brown in spots, flip and cook the second side for 2 to 3 minutes, until golden brown with additional browned spots and the bread is cooked through. Adjust the heat as needed to prevent excessive browning before the center is fully cooked.

Transfer the cooked flatbread to a clean kitchen towel and cover to keep warm and soft while repeating with the remaining dough. Directly before serving, brush both sides of each bazlama with extra-virgin olive oil, sprinkle with coarse salt, and parsley.