Preheat your oven to 350°F (175°C). This ensures that your cookies bake evenly and develop that perfect golden color.
In a large mixing bowl, add the softened unsalted butter and granulated sugar. Using an electric mixer, cream them together on medium speed until the mixture is light and fluffy, about 4-5 minutes.
Crack the two large eggs into the bowl, along with the fresh lemon juice, lemon zest, and vanilla extract. Beat the mixture until everything is well combined. The batter will be smooth and fragrant.
In a separate bowl, whisk together the all-purpose flour and baking powder. Gradually add this dry mixture to the wet ingredients, mixing on low speed until just combined. Be careful not to overmix; a few flour streaks are perfectly fine.
Using a cookie scoop or tablespoon, drop rounded balls of dough onto the prepared baking sheet, spacing them about two inches apart. If desired, sprinkle a little sparkling sugar on top of each cookie for a decorative touch.
Place the baking sheet in the preheated oven and bake for about 10-12 minutes, or until the edges are lightly golden but the centers are still soft. Remove from the oven and let the cookies cool on the baking sheet for a few minutes before transferring them to a cooling rack.
While the cookies are cooling, prepare a simple glaze by whisking together the sifted confectioners' sugar, fresh lemon juice, and milk in a small bowl until smooth. Drizzle the glaze over the cooled cookies for an extra touch of sweetness.