Preheat the oven to 350°F (175°C).
In a medium bowl, whisk together the all-purpose flour, baking powder, and salt. Set aside.
In a large bowl, beat the softened unsalted butter and granulated sugar together until light and fluffy, about 2-3 minutes.
Add the egg, fresh lemon juice, lemon zest, and vanilla extract to the butter mixture. Beat until fully combined.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Do not overmix.
Lightly grease an 8-inch oven-safe skillet with butter or non-stick spray.
Spread the cookie dough evenly into the prepared skillet, smoothing the top with a spatula.
Bake in the preheated oven for 18-20 minutes, or until the edges are golden and a toothpick inserted into the center comes out clean.
Remove the skillet from the oven and allow the cookie to cool for 10 minutes.
Dust the top of the cookie with powdered sugar before serving.