Preheat oven to 350°F (175°C). Line baking sheets with parchment paper.
In a large bowl, cream together the softened butter and granulated sugar until light and fluffy.
Beat in the eggs one at a time, then stir in the vanilla extract.
In a separate bowl, whisk together the flour, baking soda, and salt.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Do not overmix.
Roll dough into 1-inch balls and place them 2 inches apart on the prepared baking sheets.
Bake for 10-12 minutes, or until the edges are lightly golden brown.
Let cookies cool on the baking sheets for a few minutes before transferring them to a wire rack to cool completely.
While the cookies are cooling, prepare the glaze. In a small bowl, whisk together the powdered sugar, lemon juice, and lemon zest until smooth. Add more lemon juice or powdered sugar as needed to reach desired consistency.
Once the cookies are completely cool, dip the tops into the lemon glaze or drizzle it over the cookies.
Let the glaze set before serving.
Notes
Store leftover cookies in an airtight container at room temperature.