Spread the extra Mozzarella cheese (or Gruyere) over the rolled-out dough, then add the cooled mushroom filling to cover the entire dough surface.
Using the edge of the parchment paper, roll the longest edge of the dough over into a log. Wrap it in parchment paper and let it sit in the fridge for 5-10 mins.
PRO TIP: Cut the dough using dental floss.
Preheat oven to 425 F. Line a baking tray with parchment paper.Remove the log from the fridge, place it on the counter and unwrap the parchment paper. Slide a long piece of dental floss underneath the log, pull up both ends, cross them over and pull the floss gently as if you are tying a knot; let the floss wire do most of the work without force, and it will easily cut through the pastry without disturbing the shape of the pinwheel.
Carefully lift each pinwheel with a spatula and lay it flat onto the baking tray. I cut the uneven ends off first then I cut from the middle outwards to make about 10-12 pinwheels, ¾ inch thick.
Bake the pinwheels in a preheated oven at 425 degrees F for 15-20 mins. After 5 mins, the dough will begin to melt, and that's the best time to take the baking tray out and push in the edges of the pinwheels with a spatula, to retain their shape. Then return the tray to the oven to resume baking.Remove the tray from the oven once the edges of the pinwheels are lightly browned. Remove the baking tray from the oven and let the pinwheels cool in the tray. Transfer them to a plate lined with a paper towel to absorb any moisture and grease.