Preheat the oven to 350°F (175°C). Line two baking sheets with parchment paper.
In a medium bowl, whisk together the all-purpose flour, baking soda, baking powder, and salt. Set aside.
In a large bowl, using an electric mixer, cream the softened unsalted butter and granulated sugar together on medium speed until light and fluffy, about 3 minutes.
Add the egg, lemon zest, and vanilla extract to the butter and sugar mixture. Beat until well combined.
Mix in the sour cream until fully incorporated.
Gradually add the dry flour mixture to the wet ingredients, mixing on low speed until just combined. Do not overmix.
Using a tablespoon or cookie scoop, drop rounded balls of dough about 2 inches apart onto the prepared baking sheets.
Bake in the preheated oven for 9 to 11 minutes, or until the edges are lightly golden but the centers are still soft.
Remove the cookies from the oven and allow them to cool on the baking sheets for 5 minutes before transferring to a wire rack to cool completely.