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Preheat oven to 400°F with racks in upper and lower thirds. Lightly oil 2 large (17- by 13-inch) baking sheets.
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Stir together rosemary, thyme, 1/4 cup cheese, 1/2 tsp salt, and 1/4 tsp pepper in a small bowl. Stir together oil, garlic, and 1/4 tsp each of salt and pepper in another bowl.
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Divide dough in half. Keeping half of dough covered with a kitchen towel (not terry cloth), gently roll out other half into a 15- by 10-inch rectangle on a lightly floured surface with a lightly floured rolling pin. (Use your hands to pull corners. If dough is very elastic, cover with towel and let rest about 3 minutes.)
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Sprinkle one half of dough (crosswise) with half of herb mixture, then fold dough in half crosswise and roll lightly to form a roughly 10- by 8-inch rectangle. Cut lengthwise into 9 strips (less than 1 inch wide) with a pizza wheel or a sharp heavy knife. Keeping remaining strips covered with a kitchen towel, twist each strip from both ends and place on baking sheet, arranging twists 1 inch apart. Brush with 1 Tbsp garlic oil and let stand while forming remaining bread twists.
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Roll out and form more bread twists with remaining dough and herb mixture, then arrange on other sheet. Brush with 1 Tbsp garlic oil and let stand 5 minutes.
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Bake bread twists, switching position of sheets halfway through, until golden, 20 to 25 minutes total.
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Meanwhile, stir together parsley and remaining 3/4 cup cheese in a shallow baking pan.
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Immediately after baking, brush bread twists with remaining garlic oil, then roll in parsley and cheese until coated. Serve warm or at room temperature.
