Grease a large bowl with cooking spray and set aside.
In the bowl of a stand mixer fitted with the dough hook attachment, combine the water, yeast, and sugar. Let the mixture sit until it becomes foamy, about 5 minutes.
Add 2 cups of flour, 2 tablespoons of the olive oil, and the salt to the yeast mixture and mix until the dough comes together into a ball, about 5 minutes. If the dough is too sticky, add more flour, 2 tablespoons at a time, until it forms a ball. Lightly flour your work surface, then turn out the dough and knead it 10 times. Transfer the dough to the greased bowl and cover the bowl with plastic wrap. Let the dough rest in a warm, dark place until it has doubled in size, about 1 hour.
Preheat the oven to 500°F. Dust a pizza stone or baking sheet generously with cornmeal.
Lightly flour your work surface. Turn out the dough and punch it down with your hands to deflate. Using a rolling pin, roll the dough until it is 1/8 inch thick. Transfer the dough to the prepared pizza stone, prick it all over with a fork, then brush it with the remaining 1 tablespoon olive oil.
Bake the flatbread for about 7 minutes, until golden brown and slightly crisped around the edges. Remove the flatbread from the oven and set aside to cool.