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, using an electric mixer, cream the softened unsalted butter and granulated sugar together until light and fluffy, about 2-3 minutes.
Add the egg to the butter and sugar mixture and beat until fully incorporated.
Mix in the lemon zest, fresh lemon juice, and vanilla extract until combined.
Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined. Do not overmix.
Lightly grease an 8-inch oven-safe skillet or cast iron pan.
Spread the cookie dough evenly in the 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 or with a few moist crumbs.
Remove the skillet from the oven and allow the lemon cookie to cool for 10 minutes.
Dust the top with powdered sugar before serving.
Serve warm directly from the skillet or with a scoop of vanilla ice cream if desired.