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In large mixing bowl, cream together butter and 1 cup sugar until fluffy.
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Add egg and beat well.
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Sift together flour and cornstarch and add to butter mixture.
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Stir in walnuts.
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Mix well.
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Place dough in a ball in wax paper and chill for roughly 5 hours.
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Roll dough on lightly floured surface to 1/4" thickness.
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Using cookie cutters, cut out equal numbers of solid hearts and hearts with centre cut out.
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(You can either re-roll the cut out centres to make more of the larger hearts or bake them all for little bite-size cookies.) Place on ungreased cookie sheet.
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Chill for 30 minutes.
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Bake at 325 for 10- 15 minutes or until lightly browned.
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Place on rack to cool.
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While still slightly warm, spread the bottom side of the full hearts with jam- about 1/4 tsp each.
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Top with heart that has centre cut out.
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Bottoms should be together, tops facing out for a smoother look.
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(For mini hearts, spread jam on bottom of one heart and top with a second of same size- bottoms together) Sift 1/2 cup of the remaining sugar and press bottoms of cookies in sugar to coat.
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Gently sift the remaining 1/4 cup sugar over tops of cookies.