Divide the dough into 2 equal portions. Roll each portion into a rectangle approximately 1/4 inch thick.
Brush one side of each rectangle with 1/2 tablespoon of oil and season with 1/4 teaspoon of the salt and 1/4 teaspoon of the pepper.
Transfer the dough to the grill, oiled-side down. Close the cover. Cook until the dough begins to bubble on the top, about 3 minutes. Working quickly, brush each rectangle with 1/2 tablespoon of oil and season with the remaining salt and pepper.
Turn and cook until golden and crisp on the bottom, 2 to 3 minutes more. Brush each piece of flat bread with the remaining oil and sprinkle with the thyme. Cut into pieces.
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