Broiled Mint Msemen with Honey

Ingredients

• For the msemen:
• 1 pound 6 1/2 ounces all-purpose flour
• 1/2 teaspoon Diamond Crystal kosher salt; for table salt, use half as much by volume or use the same weight
• 1 teaspoon granulated sugar
• 1/4 teaspoon instant yeast
• 1 1/2 cups warm water
• 1 large egg
• 1/4 cup vegetable oil
• 1/4 cup unsalted butter
• 1 cup packed fresh mint leaves
• 1/4 cup fine semolina
• Flaky salt, such as Maldon, for sprinkling
• For the honey-butter:
• 1/2 cup honey
• 1/2 cup unsalted butter
• 1 teaspoon water
• Kosher salt

Directions

1. For the msemen, add the flour, salt, sugar, and yeast to the bowl of a stand mixer with the dough hook attached. Turn the mixer to low and pour in the water gradually. Add the egg, then mix until everything is fully incorporated. Raise the speed to medium and knead until the dough is soft, tender, and just barely tacky, about 2 minutes.
2. Move the dough into a greased mixing bowl. Rub a light coating of oil over the whole surface, cover the bowl with plastic, and place it somewhere warm until the dough has grown by about 50 percent, about 1 hour.
3. While the dough rests, put the butter and oil in a small saucepan. Warm them over medium heat until the butter has melted, then take the pan off the heat and let the mixture cool to room temperature.
4. Turn the dough out onto a lightly oiled work surface and press it down to deflate it. Slick your hands with the butter and oil mixture. Cut the dough into eight equal pieces, coating each one lightly with the butter and oil mixture as you go. Set the dough balls on a rimmed baking sheet, cover them with plastic, and let them rest until they have grown by about 50 percent, about 1 hour.
5. On a lightly oiled surface, work with one piece of dough at a time, keeping your hands greased. Press from the center outward to flatten it into an 8- by 8-inch square, aiming for an even thickness across the dough. Brush the top generously with the butter and oil mixture, scatter a large pinch of semolina over it, and add mint leaves across the surface.
6. Fold the dough into thirds, the way you would fold a letter. Brush the top again with the butter and oil mixture, add another dusting of semolina, and sprinkle with a pinch of flaky salt. Fold it into thirds again so you have a square parcel. Place the folded packets back on the baking sheet, cover them loosely with plastic, and let them rest at least 15 minutes and up to 20 minutes.
7. Meanwhile, make the honey-butter. Combine the honey, butter, and water in a small saucepan and cook over medium heat, stirring, until the butter has melted and the sauce is smooth. Season with salt, then set it aside to cool.
8. To finish, heat the broiler and position the oven rack 6 inches from the broiler element. Working with one dough packet at a time, place it on a second rimmed baking sheet. Coat your hands again with the butter and oil mixture, then use your fingers to press and stretch the packet into a roughly 6- by 6-inch square.
9. Broil the dough until it is browned in patches, flipping it once midway through, about 1 minute per side. Move it to a platter and drape a kitchen towel over the top to hold in the warmth. Continue with the remaining dough packets, letting the baking sheet cool to a safe level between uses. Serve with honey butter.