1 1/2 cups flour
1/4 teaspoon baking powder
1/8 teaspoon salt
2 small lemons
5 tablespoons butter, softened
1/2 cup sugar, plus additional for dusting
1 large egg, separated
1/2 teaspoon pure vanilla extract
2 sheets Whisk flour, baking powder, baking soda and salt in a bowl. Grate zest from 1 lemon directly over another mixing bowl. Squeeze 3 tablespoons lemon juice into a third bowl; set aside. Add butter to and beat with an electric mixer on medium until combined. Add sugar a little at a time; beat 1 minute. Add yolk (cover egg white with plastic wrap and refrigerate until ready to use) and half the flour mixture; beat on low until just combined. Add lemon juice, vanilla and remaining flour mixture. Beat until just combined. Form dough into a log about 8 inches long and 2 inches in diameter.
Cover tightly in plastic wrap. Refrigerate 3 hours.
Heat oven to 350°F. Line 2 baking sheets with parchment paper. Cut dough into 40 thin rounds and place on baking sheets. Whisk egg white with 1/4 teaspoon water; brush on top of cookies. Dust each with a bit of sugar. Bake 8 to 10 minutes or until edges are golden. (If baking both sheets of cookies at the same time, alternate positions halfway through.) Let cool on baking sheet 5 minutes. Transfer to wire racks to cool completely.