For this recipe, the dough only needs to chill about 20-30 minutes in the refrigerator since it is already rolled out. If you would rather chill the dough first before rolling, you'll want to increase the chill time to about an hour.
Using the parchment paper is a great tip for rolling the dough, because it eliminates the need to add extra flour to keep it from sticking.
My cookies were done baking in 9 minutes, but check yours closely. You want them to be just barely set and not yet browned. They'll seem slightly undercooked right out of the oven, but will firm up nicely once cooled. 9 minutes seemed to be the sweet spot for me!
Once the cookies come out of the oven, only let them stay on the baking sheet for about 5 minutes, or just until you're able to carefully slide a spatula underneath the cookies without breaking them to transfer to a cooling rack. Letting the cookies stay on the baking sheet any longer will dry them out, making them less soft and tender.