Make the dough by mixing all of the dry ingredients in the bowl of a standing mixer.
Start by adding the milk and the water and mix to form a dough. The dough should be soft and easy to knead, but not too sticky. If the dough is too sticky to handle, add a little flour 1 tablespoon at a time*.
Divide the dough into balls the size of golf balls. Pre-shape the balls making sure the surface of the balls is smooth. Transfer them onto an oiled tray, cover loosely with plastic and leave to rest for 20 minutes.
In the meanwhile put the butter, the vegetable oil and the semolina in three separate bowls ready to use when your dough is rested enough to proceed.
In order to shape the dough, you generously oil your work surface and your hands. Take one ball and dip it in the oil and place it on your workspace. Gently spread the dough into a paper-thin circle. Try to be careful not to tear the dough so oil your hands as often as needed so that they slide easily over the dough.
Dot the flattened dough with butter and sprinkle with semolina. Fold the dough into thirds like a letter to form an elongated rectangle. Dot again with butter, sprinkle with semolina, and fold again into thirds to form a square. Once the msemmen is folded, another is spread that one is used to envelope a prior folded msemmen so as to create multiple internal layers of dough. Leave to rest a short while before flattening and cooking. Transfer the folded dough to the oiled tray and repeat with the remaining balls of dough. Keep track of the order in which you folded the squares. Let the dough envelopes rest for 30 minutes, but start the timer when you finished your first envelope.
Heat your griddle or frying pan over medium heat until quite hot. Starting with the first msemmen you folded, take a square of dough and place on your oiled work surface. Oil your hands and pat the dough firmly to flatten it to double its original size.
Transfer the flattened square to the hot griddle and cook, turning several times, until cooked through, crispy on the exterior and golden in color. Transfer to a rack.
Repeat with the remaining squares, working with them in the order in which they were folded. Serve the msemmen immediately, or allow to cool completely before freezing**.
* The amount of water needed depends on the quality of absorption of the flour you are using.
**Msemmen can be reheated directly from the freezer in a frying pan placed over medium-low heat.