In a bowl toss together Parmesan, spices, and salt. On a lightly floured surface roll out pastry sheet into a 16- by 10-inch rectangle and brush with some egg wash. Cut pastry in half crosswise, forming two 10- by 8-inch rectangles. Sprinkle Parmesan mixture over 1 rectangle and top with other rectangle, egg-wash side down, pressing firmly to force out any air pockets. Roll out pastry slightly to make layers adhere (rectangle should be about 10 1/2 by 8 1/2 inches). Brush pastry with some egg wash and with a sharp large knife or pastry wheel cut lengthwise into 1/4-inch-wide sticks.

Arrange cheese straws about 1 1/2 inches apart on baking sheets, pressing ends onto baking sheets. Bake cheese straws in batches in middle of oven until golden, about 10 minutes. Transfer cheese straws to a rack and cool. Cheese straws may be made 2 days ahead and kept in an airtight container. Recrisp cheese straws in a 425° F. oven until heated through, about 5 minutes.

Makes about 36 cheese straws