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Stir chocolate in top of double boiler over simmering water until smooth; cool.
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Combine flour and next 5 ingredients in medium bowl.
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Using electric mixer, beat 1 3/4 cups sugar and butter in large bowl until light.
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Beat in eggs 1 at a time, then vanilla and chocolate.
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Gradually add dry ingredients, beating just until combined.
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Chill dough until firm, about 2 hours.
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Preheat oven to 350°F.
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Lightly butter 2 large baking sheets.
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Place powdered sugar in shallow pan.
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Form dough into 1-inch balls.
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Roll each ball in sugar to coat; shake off excess sugar.
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Arrange cookies on prepared baking sheets, spacing 1 1/2 inches apart.
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Press 1 cherry half into center of each cookie.
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Bake until cookies puff and crack but are still soft, about 10 minutes.
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Transfer cookies to rack and cool completely.
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(Cookies can be prepared ahead. Store in airtight container at room temperature up to 1 week, or freeze up to 1 month.).