Heat the oven to 375 degrees and line two baking sheets with parchment.
Lay the puff pastry on a lightly floured surface. Roll it into a rectangle about 14 by 10 inches that's about 1/8 inch thick.
Working quickly, brush the mustard over the entire sheet of dough. Sprinkle the cheese evenly over the mustard, followed by the pepper if using.
Starting with one of the short sides of the rectangle, roll the dough into a compact log. (At this point you can wrap the log and keep it in the refrigerator or the freezer until you're ready to bake the pinwheels.)
To make the pinwheels, using a very sharp knife slice the log into 1/4-inch wheels and arrange them at least an inch apart on the baking sheets. Bake the pinwheels for about 10 minutes, until they are golden brown and crisp. Let them cool for a few minutes before serving.