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Preheat oven to 325° and butter 2 baking sheets.
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Beat sugar and butter. Add eggs 1 at a time, beating well.
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Add orange peel and vanilla; beat.
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Add dry ingredients to butter mixture, mixing until just incorporated.
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Divide dough into 2 parts.
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Form into logs and flatten to 1 1/2-inch thick with lightly-floured hands on baking sheets.
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Bake until firm, about 30 to 35 minutes. Cool 15 minutes.
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Using serrated knife, cut into 1/2-inch slices. Return to the oven and bake on both sides until golden (about another 8 minutes per side). Cool.