In a large mixing bowl, beat together the softened unsalted butter and granulated sugar until light and fluffy. This process should take about 3-4 minutes at medium speed using an electric mixer.
Once your butter and sugar mixture is fluffy, add in the large egg along with the lemon zest and lemon juice. Beat on low speed until fully mixed in.
In another bowl, whisk together all-purpose flour, baking powder, baking soda, and salt until evenly combined. Gradually add this dry mixture into the wet ingredients while mixing on low speed until just combined.
Scoop tablespoon-sized portions of dough onto lined baking sheets, leaving space between each ball. Bake in a preheated oven at 350°F (175°C) for about 10-12 minutes or until edges are lightly golden but centers remain soft.
While cookies cool down completely, prepare your frosting by beating together softened unsalted butter, powdered sugar, lemon zest, and fresh lemon juice in a separate bowl until creamy and smooth.
Once cooled completely, generously frost each cookie with the prepared lemon frosting using a spatula or piping bag if desired.