Preheat your oven to 350°F (175°C).
Line your baking sheets with parchment paper to prevent sticking and for easy cleanup.
In a medium bowl, whisk together the all-purpose flour, baking powder, baking soda, and salt.
In a large mixing bowl, cream together the softened unsalted butter and granulated sugar using an electric mixer until light and fluffy, about 3-4 minutes.
Beat in the eggs one at a time, fully incorporating each before adding the next. Then mix in the sour cream, lemon zest, and vanilla extract until well combined.
Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined. Avoid overmixing.
Drop rounded tablespoons of dough onto the prepared baking sheets about 2 inches apart using a cookie scoop or tablespoon.
Bake for 10-12 minutes, until edges are lightly golden. Centers may appear slightly underbaked but will firm as they cool.
Allow cookies to cool on the baking sheet for 5 minutes, then transfer to a cooling rack to cool completely.
In a medium bowl, whisk together the powdered sugar, softened cream cheese, and fresh lemon juice until smooth and creamy. Adjust consistency as needed.
Once cookies are completely cooled, drizzle the glaze over the tops using a spoon or piping bag.