Crispy Parmigiano Flatbread

Combine the yeast and warm water in a small bowl and set aside until foamy, about 5 minutes. Stir in the olive oil.

Put the flour and salt in the bowl of an electric mixer fitted with the dough hook or in a large bowl. Pour in the yeast mixture and mix on low speed or with your hands until the water is absorbed and a shaggy dough is formed. Knead the dough on a lightly floured board until the dough is uniform and smooth, 2 to 3 minutes. The dough will be slightly sticky.

Divide the dough into 4 equal pieces and shape them into balls. Dust the balls with flour and place them on a lightly floured baking sheet. Cover with plastic wrap and let the dough rise in a warm place until doubled in size, 1 to 2 hours. (The dough can be stored in an airtight container for up to 2 days.)

Preheat the oven to 425°F (220°C). Have ready 2 nonstick baking sheets or slick two regular baking sheets with olive oil.

Working with 1 dough ball at a time (cover the remaining dough with a moist kitchen towel until ready to use), dust the ball with flour and flatten it with your hand. Cut the dough in half and roll half the dough through a pasta machine with the rollers set midway apart. Dust the dough with flour if it becomes sticky. Decrease the space between the rollers one setting at a time until you have reached the last setting and the dough is a smooth, thin sheet. Transfer to a cutting board and cut in half on an angle into large pieces so that 2 will fit on a cookie sheet. The pieces should each be approximately 4 inches wide and 12 inches long. Roll and cut the remaining half in the same manner as the first.

Place the rolled dough on the baking sheets. Brush lightly with olive oil, sprinkle with about a quarter of the cheese, and bake until golden brown, 12 to 14 minutes. Transfer to a wire rack to cool. Repeat with the rest of the dough balls, rolling and baking until all the dough is used.