Step 1

For Cookies: Sift first 7 ingredients into medium bowl. Using electric mixer, beat butter in large bowl until fluffy. Add sugar and beat until well blended. Beat in molasses, egg yolk, orange peel, and vanilla. Add flour mixture and beat just until blended. Gather dough into ball. Divide into 4 pieces. Flatten each into disk. Wrap each in plastic and chill until cold and firm, at least 4 hours.

Step 2

Position racks in top third and bottom third of oven and preheat to 350 degrees. Line 2 baking sheets with parchment paper. Roll out 1 piece of dough on lightly floured surface to 1/4-inch thickness. Using 2 1/2- to 3-inch star-shaped cutter, cut out cookies. Transfer cookies to prepared sheets, spacing 1/2 inch apart (cookies spread very little). Gather scraps and reroll dough, cutting out more cookies.

Step 3

Bake cookies 5 minutes. Reverse baking sheets; bake until cookies are puffed and look slightly darker around edges, about 5 minutes longer. Cool cookies on sheets 2 minutes. Using thin metal spatula, transfer cookies to racks; cool. Repeat with remaining dough pieces.

Step 4

For Icing: Sift 1 1/2 cups sugar into medium bowl. Add 5 teaspoons water and vanilla; whisk until smooth. Whisk in more sugar by tablespoonfuls, if necessary, until icing falls thickly off whisk. Spoon icing into pastry bag fitted with 1/16-inch plain round tip or resealable plastic bag (cut tip off bag). Pipe icing onto cookies. Let stand until icing is hard, at least 3 hours. (Can be made 2 days ahead. Store airtight between sheets of waxed paper.)