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In large bowl of an electric mixer, beat 1 cup of the sugar and butter until well blended.
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Add lemon peel and juice; mix to blend.
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Beat in eggs, 1 at a time, until smooth.
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Gradually stir in 3 cups of the flour, mixing well. cover and chill until dough is firm enough to handle easily, at least 3 hours or as long as 2 days.
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For easier handling, chill the dough before you form the ring-shaped cookies.
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Divide dough in half. Cover and chill 1 portion.
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Divide other half into 8 equal pieces. With floured fingers, roll each piece on a lightly floured board to make a 10-inch rope.
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Overlap ends of each rope slightly to form a ring.
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Place rings about 1 inch apart on a greased 14x17 inch baking sheet. Sprinkle light with sugar. Bake in a 300°F oven until golden, 35-40 minutes.
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Remove cookies from pans and let cool completely on racks. Repeat with remaining dough.
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Serve or store airtight up to 10 days.