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Preheat oven to 350°F.
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Place brown sugar in large mixing bowl; set aside. In medium skillet, melt butter over medium heat. Watching closely, cook until butter is just golden brown. Pour over brown sugar; cool to room temperature.
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In large bowl, whisk together flour, baking soda, cream of tartar, and salt. Set aside.
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Beat butter and brown sugar mixture at medium speed until combined. Beat in eggs one at a time; add vanilla.
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Add flour mixture; beat at low speed just until combined. Stir in nuts.
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Divide dough into 3 pieces. Roll each piece into 8-inch log; wrap each log in plastic wrap.
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Chill until firm, at least several hours. Slice logs 1/4 inch thick. Place 2 inches apart on parchment-lined baking sheets.
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Bake about 8 to 10 minutes, until set. Cool on wire racks and store in airtight containers.