In a stand mixer with the paddle attachment blend the goat cheese and butter until smooth. Add the thyme, zest, and 1/4 teaspoon salt. Taste a bit, and season with more salt, if needed and add a few grinds of pepper. Add the flour and blend until smooth. Remove the dough and using a piece of plastic wrap to guide and mold, roll the dough into an 8-inch long log. Refrigerate for 2 hours.
Heat the oven to 325 degrees F.
Remove the dough log from the refrigerator and cut into 1/3-inch discs. Place on an ungreased parchment paper-lined baking sheet, about an inch apart. Bake until golden on top and set, 30 to 35 minutes. Remove from the oven and slide the parchment off of the baking sheet and onto a cooling rack with the crackers still attached. Cool completely before eating.
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