Rub zest into 3/4 cup sugar with clean fingertips until fragrant. Beat with butter until creamy; add egg, lemon juice, and vanilla.
Whisk flour, baking powder, and salt; mix into butter just until combined. Cover; refrigerate 1 hour, additional to active prep time.
Heat oven to 350°F; line two sheets. Form chilled dough into 24 balls; roll in coating granulated sugar, then powdered sugar.
Bake one sheet at a time 11 to 12 minutes until tops cracked and rims set without dark browning.
Cool on sheets 5 minutes; rack-cool before stacking.