Preheat your oven to 350°F (175°C). Line a 9x13-inch baking dish with parchment paper, leaving some overhang on the sides for easy removal later.
In a food processor, pulse together flour, sugar, and salt until combined. Add the cold cubed butter and pulse until the mixture resembles coarse crumbs (about 10-12 pulses). Add the egg yolk and vanilla extract, then pulse just until the dough begins to come together.
Transfer the dough mixture to your prepared baking dish. Using your fingers or the bottom of a measuring cup, press the dough evenly into the bottom of the pan. Prick the crust all over with a fork to prevent bubbling.
Bake the crust for 15-18 minutes until the edges are just beginning to turn golden. Remove from oven but keep the oven on.
While the crust is baking, whisk together the pumpkin puree, heavy cream, eggs, brown sugar, pumpkin pie spice, salt, and vanilla extract in a large bowl until smooth and well combined. For the silkiest texture, use a hand mixer on low speed for 1-2 minutes.
Pour the pumpkin filling over the warm pre-baked crust, spreading it evenly with a spatula. Gently tap the pan on the counter a few times to release any air bubbles.
Return to the oven and bake for 30-35 minutes, or until the center is just set with a slight jiggle (similar to gelatin). Don't overbake, as this can cause cracks in your filling.
Allow the bars to cool completely in the pan at room temperature (about 1 hour), then refrigerate for at least 1 hour or overnight before cutting.
Once fully chilled, use the parchment paper overhang to lift the entire dessert out of the pan. Place on a cutting board and slice into 16-20 bars using a sharp knife. For the cleanest cuts, wipe the knife clean between each slice.