Preheat your oven to 350°F (175°C). Line an 8×8 inch or 9×9 inch square baking pan with parchment paper, leaving an overhang on the sides. This will make it much easier to lift the bars out once they are cooled.
In a medium bowl, combine the graham cracker crumbs, melted butter, and 1/4 cup of granulated sugar. Mix until the crumbs are evenly moistened. Press the mixture firmly into the bottom of the prepared baking pan using the bottom of a measuring cup or your fingers.
Place the pan in the oven and bake the crust for 8 to 10 minutes, or until it is lightly golden and set. Remove from the oven and let it cool slightly while you prepare the filling.
In a large bowl, whisk together the pumpkin puree, sweetened condensed milk, eggs, pumpkin pie spice, vanilla extract, and 1/2 teaspoon of salt. Continue whisking until the mixture is completely smooth and no streaks of egg remain.
Pour the pumpkin mixture over the pre-baked crust. Smooth the top with a spatula. Return the pan to the oven and bake for 30 to 35 minutes. The center should be set but still have a very slight jiggle when the pan is moved. Remove from the oven and let the bars cool completely in the pan on a wire rack.
Once the bars are fully cooled, lift them out of the pan using the parchment paper overhang. Drizzle the caramel sauce generously over the top in a zigzag pattern. Sprinkle the flaky sea salt evenly over the caramel. Slice into 16 squares and serve.