Preheat oven to 350°F (175°C).

For the crust: In a medium bowl, whisk together the flour, granulated sugar, and salt. Cut in the cold butter until the mixture resembles coarse crumbs. Press firmly into the bottom of a 9x13-inch baking pan.

Bake the crust for 15 minutes.

For the filling: While the crust bakes, whisk together the pumpkin puree, eggs, evaporated milk, brown sugar, pumpkin pie spice, and vanilla extract in a large bowl until smooth.

Pour the filling over the hot crust. Bake for an additional 35-40 minutes, or until the center is just set (it should still have a slight jiggle).

Let the bars cool completely on a wire rack for at least 1 hour. Then, transfer to the refrigerator to chill for at least 4 hours or overnight before cutting and serving.