Heat oven to 450° F. On a lightly floured surface, roll and stretch the dough into a ¼-inch-thick circle or rectangle.
Sprinkle a baking sheet with the cornmeal and place the dough on top.
In a large bowl, combine the leeks, potatoes, thyme, 1 ½ tablespoons of the oil, ¾ teaspoon salt, and ½ teaspoon pepper.
Scatter vegetables over the dough and sprinkle with the Gruyère. Bake until the crust is golden and potatoes are tender, 20 to 25 minutes. Cut into pieces.
Drizzle the greens with the remaining 1 ½ tablespoons of oil and season with ¼ teaspoon each salt and pepper. Serve with the flat bread.