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.
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.
Meanwhile, preheat the oven to 350 degrees F. Cut the log into 3/8-inch-thick rounds with a small, sharp knife and place them on a sheet pan lined with parchment paper. Bake for 22 minutes, until very lightly browned. Rotate the pan once during baking. Cool and serve at room temperature.
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