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Line two baking sheets with nonstick baking mats; set aside.
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In a small bowl, mix together both cheeses and cayenne pepper, if using. Sprinkle cheese mixture on work surface; top with puff pastry and roll out to a 10-by-13-inch rectangle, pressing dough into cheese to adhere. Sprinkle top of dough with poppy seeds, if desired; press gently with a rolling pin to adhere.
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Using a pastry cutter, trim sides to form a 9-by-12-inch rectangle. Cut puff pastry into 3/4-inch-thick strips. Grab each end of a dough strip with your fingers and carefully stretch and twist strip in opposite directions; arrange 1 1/2 inches apart on prepared baking sheets. Transfer to refrigerator to chill, about 45 minutes.
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Preheat oven to 375 degrees.
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Transfer baking sheets to oven and bake until golden and puffed, 20 to 25 minutes. Transfer to a wire rack to cool.