How to Make It
Place all-purpose flour, 1 3/4 cups water, salt, 1/2 cup plus 2 tablespoons semolina flour, and 2 teaspoons oil in a stand mixer fitted with a dough hook attachment; mix on low speed until combined, about 2 minutes. Increase speed to medium, and continue mixing until dough is smooth, shiny, and elastic and pulls away from sides of bowl, about 6 minutes.
Generously coat a rimmed baking sheet with oil. Coat a large smooth work surface with oil. (A granite, stainless steel, or Formica countertop is ideal.) Transfer dough to oiled surface. Using oiled hands, divide dough into 12 (3-ounce) balls. Place balls 2 inches apart on prepared baking sheet, rolling in oil to coat. Cover loosely with plastic wrap; let rest at room temperature at least 30 minutes or refrigerate up to 8 hours or overnight. Let the dough stand at room temperature for 30 minutes before proceeding.
Meanwhile, stir together melted butter and remaining 6 tablespoons oil in a small bowl; set aside.
Re-oil work surface. Working with 1 dough ball at a time, flatten dough with the palm of your hand. Continue to apply downward pressure with your palm to stretch dough into a 10-inch circle. (Dough round should be so thin that it is translucent.) Brush dough surface with 1 tablespoon butter-oil mixture; sprinkle with 1 teaspoon semolina flour. Fold the top, bottom, and 2 side edges of dough round in toward center so dough forms a 3-inch square and edges overlap in the middle. Return dough square, seam side down, to baking sheet. Repeat process with remaining dough balls, remaining butter-oil mixture, and remaining semolina flour. Let dough squares rest at room temperature 15 minutes.
Proceeding in the same order in which you formed them, place each dough square on a lightly oiled parchment paper sheet. Stretch dough with the palm of your hand until it has slightly more than doubled in size (making about a 7-inch square). (If dough squares resist stretching, allow to rest a bit more before proceeding.) Cut parchment so that it extends just slightly beyond the square. (Do not stack dough squares as you stretch them—they will stick together.)
Heat a large griddle over medium-high until very hot. (To test, flick a drop of water onto griddle. Griddle is hot enough when the drop of water sizzles away almost immediately.) Place 2 to 3 dough squares (depending on size of your griddle), parchment side up, on hot griddle. Peel off parchment as dough begins to firm on griddle. (Parchment should easily peel off.) Cook until browned, 2 to 3 minutes per side. Transfer to a wire rack. Repeat process with remaining dough squares.
M’smen are most delicious when eaten warm, but once cooled they can be stored up to 5 days in an airtight container in the refrigerator. They freeze well up to 3 months. Reheat m’smen in a hot, dry skillet 1 minute on each side before serving.