Sprinkle yeast over lukewarm water and stir to combine. Let sit until frothy, about 10 minutes.
In the bowl of a stand mixer fitted with a dough hook or a large bowl, combine the flour, semolina, sugar, and salt.
Slowly pour in the frothy yeast with water and mix until dough comes together. If too crumbly, add a little more water. If too sticky, add a little more flour.
Knead until elastic and smooth, then divide the dough into 10 equal pieces and form each into a ball. Allow to rest, covered, for 15 minutes.
Coat your work surface and hands with vegetable oil. Using oiled hands, flatten a ball and press the dough into a thin square. You should be able to see the work surface through the dough. If it starts to stick too much to the work surface, add more oil.
Rub a thin layer of butter over the flattened dough and sprinkle with semolina. Fold the dough into thirds to form a long rectangle, continuing to coat in a little butter and semolina. Fold the right side of the rectangle over into the center, then fold the left over to cover and form a square. Repeat with remaining dough, then cover and allow to rest for another 15 minutes.
Grease a large skillet with vegetable oil and place over medium low heat.
Gently flatten the folded square of dough with oiled hands into a thin square flatbread. Place on the heated skillet and cook until golden. Flip and cook the other side until golden and cooked through. Adjust heat between medium and low as needed. Repeat with remaining squares of dough, greasing the skillet with more oil as needed.