Preheat your oven to 350°F (175°C). Line a baking sheet with parchment paper.

In a medium bowl, whisk together the flour, baking powder, baking soda, and salt. Set aside.

In a large mixing bowl, cream together the softened butter and granulated sugar with an electric mixer on medium speed until light and fluffy, about 2-3 minutes.

Add the egg, lemon zest, Meyer lemon juice, and vanilla extract to the butter mixture, mixing until combined.

Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined.

Using a cookie scoop or tablespoon, drop the dough onto the prepared baking sheet, spacing cookies about 2 inches apart.

Bake in the preheated oven for 10-12 minutes, or until the edges are lightly golden and the centers appear set.

Remove from the oven and allow to cool on the baking sheet for a few minutes before transferring to a wire rack to cool completely.

While the cookies cool, prepare the icing by whisking together the powdered sugar and Meyer lemon juice until smooth.

Drizzle the icing over the cooled cookies and allow it to set before serving.