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