For the lemon and cranberry shortbread dough: Preheat the oven to 350 degrees F. Line a 9-by-13-inch pan with aluminum foil (with a 2-inch overhang on all four sides) and grease the bottom and sides with butter.
In a small bowl, combine the flour and baking powder. Set aside. In the bowl of a stand mixer fitted with a paddle attachment, cream the butter with the sugar and vanilla on medium-high speed until light and fluffy, about 4 minutes. Add the dry ingredients and mix on medium-low until incorporated. Mix in the cranberries and lemon zest.
Press the mixture into the bottom of the prepared pan. Bake until slightly brown, about 25 minutes.
For the filling: While the shortbread is baking, whisk together the sugar, eggs, lemon juice, flour, baking powder and salt in a medium bowl. Pour the filling over the baked crust and continue baking until the filling sets and is slightly brown on the edges, about 20 minutes
Let cool completely in the pan. Use the foil edges to help lift the bar out of the baking pan. Cut into 24 squares and dust with confectioners' sugar.