¼ cup warm water (110 to 115 degrees F)
1 large egg, lightly beaten
½ cup room-temperature water
3¼ cups all-purpose flour
2 teaspoons kosher salt
1 tablespoon plus 1 teaspoon granulated sugar
¼ cup Clarified butter at room temperature
Extra virgin olive oil
Maldon salt or fleur de sel
Combine the warm water and yeast in a small bowl. Let stand for 10 minutes, then stir to dissolve the yeast. Mix the egg with the water and stir to combine with the yeast mixture.
Combine the flour, salt, and sugar in the bowl of a stand mixer fitted with the dough hook. With the mixer on low speed, add the butter, followed by the egg mixture, and mix until the dough comes together on the hook.
Transfer the dough to a lightly floured board and knead for 5 minutes, or until smooth. Fold the edges under to form a round dough. Lightly oil a large bowl with canola oil and put the dough in the bowl. Brush a piece of plastic wrap with canola oil and press it directly onto the surface of the dough. Cover the bowl with a kitchen towel and let sit in a warm place until doubled in size, about 2 hours.
Position the oven racks in the lower and upper thirds of the oven and preheat the oven to 350 degrees. Line two baking sheets with parchment paper and brush with olive oil.
Open the rollers of a pasta machine to the widest setting and flour the rollers. Cut the dough in quarters. Work with one quarter at a time, keeping the other pieces covered so they do not dry out. Lightly flour the piece of dough and, using the heel of your hand, press the dough down to a rectangle about ½ inch thick. Trim off one end so there is a straight edge, and roll the dough through the machine. Roll again through the widest setting. Continue to roll the dough twice through each setting, lightly flouring it as needed to keep it from sticking, until it is paper-thin; we roll ours to the second-to-last setting.
The piece of dough will be about 36 inches long. Trim the ends. Cut lengthwise in half and the cut crosswise in half to make 4 sheets about 3 inches by 15 inches. Place 3 sheets on one of the lined baking sheets, and roll out a second piece of dough. (If you don’t have three baking sheets, put the extra sheets of dough on a sheet of parchment paper until ready to bake.)
Brush the flatbreads lightly with olive oil and sprinkle with Maldon salt and if using, piment d’Espelette. Bake for 12 to 15 minutes, switching the position of the pans and rotating them halfway through baking, until crisp and golden. Let the flatbreads cool on the pans on cooling racks.
Repeat with the remaining dough. Leave the breads whole or break into pieces and serve. Store in an airtight container for up to 1 week.
Makes 16 sheets of flatbread 15 inches by 3 inches.