1/2 cup (1 stick) unsalted butter, room temperature
1/4 cup powdered sugar
2 teaspoons (packed) finely grated lemon peel
1/2 teaspoon vanilla extract
1 cup all purpose flour
Generous pinch of coarse kosher salt
2 teaspoons (about) sugar
Additional powdered sugar (optional)
1) Line 2 large rimmed baking sheets with parchment paper. Using electric mixer, beat butter and 1/4 cup powdered sugar in medium bowl until smooth. Beat in lemon peel and vanilla. Add flour and coarse salt and beat just until blended. Transfer dough to large piece of plastic wrap and press into disk. Cover dough with another piece of plastic wrap and roll out dough to 1/4-inch thickness. Place wrapped dough on another baking sheet and chill until firm, 20 to 30 minutes.
2) Position 1 rack in top third and 1 rack in bottom third of oven and preheat to 350 degrees F. Transfer wrapped dough to work surface; remove top sheet of plastic. Using a 2 to 2-1/2-inch heart-shaped cookie cutter dipped in flour, cut out cookies and place on 1 parchment-lined baking sheet, spacing 1 to 1-1/2 inches apart. Reroll dough scraps to 1/4-inch thickness and cut out additional cookies; place on second parchment-lined baking sheet. Sprinkle top of cookies lightly with sugar (about 2 teaspoons). Chill 10 minutes.
3) Bake cookies until light brown on bottom and just barely golden around edges, about 15 minutes. Transfer cookies to rack and cool completely. Sift powdered sugar lightly over top of cookies, if desired. These can be made 3 days ahead. Store in single layer in airtight container at room temperature. Yield: 12 to 16 cookies.
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