Preheat the oven to 350°F (175°C) and line an 8x8-inch baking pan with parchment paper.

In a mixing bowl, combine gluten-free flour, sugar, and salt. Cut in cold butter until resembling coarse crumbs. Add the egg and mix until a dough forms. Press this dough into the bottom of the pan.

In a separate bowl, whisk together pumpkin puree, brown sugar, eggs, evaporated milk, vanilla, and pumpkin pie spice until smooth.

Pour the filling over the crust and tap the pan to release air bubbles. Bake for 40-45 minutes, or until the edges are set and the center is slightly jiggly.

Allow the bars to cool completely on a wire rack, then lift out using the parchment overhang and cut into squares for serving.