Place an oven rack in the center of the oven. Preheat the oven to 450 degrees F. Dust a heavy baking sheet with cornmeal. Set aside.
On a lightly floured work surface, roll out the dough into a 1/4-inch thick rectangle about 16 inches long and 8 inches wide. Transfer the dough to the prepared baking sheet.
In a large skillet, heat the oil over medium-high heat. Add the leeks and season with salt and pepper. Cook, stirring frequently until tender, about 5 minutes. Add the garlic and cook for 30 seconds until aromatic. In batches, add the spinach and cook until wilted, about 5 minutes. Remove the pan from the heat and add the feta cheese and mint. Season with salt and pepper, to taste.
Using the tines of a fork, prick the surface of the dough all over. Spread the spinach mixture on top and dot with butter.
Bake until the dough is golden and crunchy, 15 to 18 minutes. Cut into squares and serve.