Preheat the oven to 350°F (175°C). Grease a 10-inch oven-safe skillet with butter or non-stick spray.
In a large bowl, cream together the softened butter, granulated sugar, and powdered sugar until light and fluffy, about 3-4 minutes.
Add the eggs one at a time, beating well after each addition.
Mix in the lemon zest and fresh lemon juice until fully incorporated.
In a separate bowl, whisk together the all-purpose flour, baking powder, baking soda, and salt.
Gradually add the dry ingredients to the wet ingredients, mixing just until combined.
Fold in the white chocolate chips evenly throughout the dough.
Transfer the cookie dough to the prepared skillet and spread it evenly with a spatula.
Bake in the preheated oven for 22-25 minutes, or until the edges are golden and a toothpick inserted in the center comes out clean or with a few moist crumbs.
Remove from the oven and allow to cool in the skillet for 10 minutes before serving.