Preheat the oven to 350°F. Line two baking sheets with parchment paper.

Whisk flour, baking powder, and salt in a small bowl. Set aside.

In a large bowl, use an electric mixer fitted with the paddle attachment to beat together the butter, sugar, and lemon zest until light and fluffy, about 3 to 4 minutes, scraping down the bowl at least once. Beat in egg until very well combined, about 1 minute. Scrape down the bowl. On low speed, add the flour mixture and blend until just incorporated. Dough will be slightly dry.

Using a medium spring-loaded cookie scoop, drop 1 rac{1}{2}-tablespoon sized balls of cookie dough onto prepared baking sheets, spacing 2 inches apart. Roll each ball with your palms, then using your palm, gently flatten dough to about 1/3-inch thick.

Bake for 12-14 minutes or until cookies are just set and slightly golden brown at the edges. Cool cookies on baking sheet for 5 minutes and transfer to cooking racks. Cool completely.

Make the glaze: In a medium bowl, whisk together powdered sugar and lemon juice, a tablespoon at a time, until a very thick but pourable glaze forms. Spoon each cookie with the lemon glaze. Garnish with extra lemon zest, if desired.