Preheat oven to 375 degrees.
Lay out the prepared refrigerated pizza dough and cut it into 3 equal strips lengthwise.
Put a handful of shredded cheddar and mozzarella cheese on top of each strip.
Roll the strips up to make long tubes of cheese-filled dough, then fold them into the shape of pretzels.
Place the pretzels on baking sheets and brush with egg wash.
Cover liberally with Parmesan cheese.
Bake at 375 degrees for 15 to 18 minutes.
Remove and let cool for about 5 minutes.
Serve with dipping sauce.