1. In the bowl of an electric mixer fitted with the paddle attachment, cream the butter for 1 minute. With the mixer on low speed, add the Parmesan, thyme, salt, and pepper and combine. With the mixer still on low, add the flour and combine until the mixture is in large crumbles, about 1 minute. If the dough is too dry, add 1 teaspoon water.
2. Dump the dough onto a floured board, press it into a ball, and roll into a 9-inch log. Wrap in plastic and refrigerate for at least 30 minutes or for up to 4 days.
3. Meanwhile, preheat the oven to 350 degrees F and line a baking sheet with parchment paper. Cut the log into 3/8-inch-thick rounds with a small, sharp knife and place them on the baking sheet. Bake for 22 minutes, rotating the pan 180 degrees halfway through baking, until very lightly browned. Cool and serve at room temperature.