Mix 3½ cups of all-purpose flour, half of 1 cup of fine semolina, 2 teaspoons of sugar, 2 teaspoons of salt, and ¼ teaspoon of dry yeast. Add 1½ cups of warm water and knead into a smooth, soft dough.
Divide into 20 plum-sized balls. Cover loosely and rest for 10-15 minutes.
Set out 1 cup of vegetable oil, ¼ cup of very soft unsalted butter, and the remaining semolina. Oil the work surface and your hands, and spread a ball out very thin.
Dot with butter, sprinkle with semolina, and fold into thirds, then into thirds again to make a square. Repeat with the rest of the balls.
Heat a griddle or frying pan over medium heat until quite hot. Flatten each square to about 4in / 10cm and cook, turning several times, until cooked through, crisp, and golden.