Preheat the oven to 350 F and line a 9x13-inch baking pan with parchment paper, leaving an overhang on two sides. For the dough, whisk together the gluten free 1-to-1 baking flour, 2 tablespoons sugar, baking powder, and salt. Cut in the cold butter using a pastry cutter or your fingers until the mixture resembles coarse crumbs. Stir in the cold milk until a soft dough forms.
Divide the dough in half. Press one half evenly into the bottom of the prepared pan using damp fingers. Set the other half aside.
Beat the cream cheese, 1/2 cup sugar, and vanilla extract with an electric mixer until smooth and creamy. Spread the filling evenly over the dough layer in the pan.
On a piece of parchment paper, pat the remaining dough into a rough rectangle the size of the pan. Carefully flip it on top of the cream cheese layer and peel off the parchment. Press gently to cover the filling.
Brush the top with melted butter. Mix 1/4 cup sugar and the cinnamon together, then sprinkle evenly over the buttered top.
Bake for 30 to 35 minutes until the top is golden and the edges are set. Let cool completely in the pan, then refrigerate for at least 1 hour before slicing into bars.