Lemon Sugar Cookies

Ingredients (12)

• 270g granulated sugar (9 1/2 ounces; 1 1/4 cups)
• 6g (2 tablespoons) packed grated lemon zest plus 1 1/2 tablespoons fresh juice from 4 large lemons, divided
• 227g (2 sticks) unsalted butter, softened
• 1 large egg, room temperature
• 5g (1 teaspoon) vanilla extract
• 320g all-purpose flour (about 11 1/4 ounces; 2 1/2 cups)
• 1/2 teaspoon baking powder
• 1/2 teaspoon Diamond Crystal kosher salt; for table salt, use half as much by volume
• 140g sifted powdered sugar (about 5 ounces; 1 1/2 cups)
• 3 tablespoons fresh lemon juice from 1 large lemon
• 1/4 teaspoon vanilla extract
• Lemon zest, for garnish