Preheat the oven to 350 degrees F (175 degrees C). Line a 9x13-inch baking pan with aluminum foil.

Mix shortbread crumbs, flour, and brown sugar in a medium bowl. Cut in butter using 2 knives or a pastry blender until mixture resembles coarse crumbs. Press over the bottom of the prepared pan.

Bake in the preheated oven for 15 minutes.

Meanwhile, beat cream cheese and white sugar using an electric mixer until well blended. Add eggs and flour. Mix well. Blend in lemon juice, lemon zest, and baking powder. Pour filling over the crust.

Bake in the preheated oven until center is set, 25 to 28 minutes. Let cool completely, at least 45 minutes. Refrigerate until well chilled, about 2 hours. Sprinkle with confectioners' sugar right before serving.