Preheat the oven to 350°F. Line an 8x8-inch baking pan with parchment paper, leaving enough overhang to easily lift the bars from the pan.
In a medium bowl, combine the flour, granulated sugar, and salt. Stir together the melted butter and vanilla, then pour into the dry ingredients and mix until a soft, crumbly dough forms.
240 g all-purpose flour, 200 g granulated sugar, 170 g unsalted butter, ½ teaspoon salt, 1 teaspoon vanilla extract
Press approximately two-thirds of the dough firmly and evenly into the bottom of the prepared pan, reserving the remaining dough for the crumble topping.
Bake the crust for 12-15 minutes, until lightly golden around the edges and dry on top. Remove from the oven and let cool for about 5 minutes while you prepare the pumpkin filling.
In a medium bowl, whisk together the pumpkin puree and brown sugar until smooth. Add the egg and egg yolk and whisk until completely incorporated.
245 g pumpkin puree, 100 g light brown sugar, 1 large egg, 1 large egg yolk
Add the heavy cream, vanilla, cinnamon, ginger, nutmeg, cloves, salt, and flour. Whisk just until the filling is smooth and evenly combined.
90 g heavy cream, 1 teaspoon vanilla extract, 1½ teaspoons ground cinnamon, ½ teaspoon ground ginger, ¼ teaspoon ground nutmeg, ⅛ teaspoon ground cloves, ¼ teaspoon fine sea salt, 8 g all-purpose flour
Pour the pumpkin filling over the warm par-baked crust and spread it into an even layer.
Crumble the reserved shortbread dough evenly over the pumpkin filling, keeping some pieces fairly large for chunky, bakery-style crumbles.
Return the pan to the oven and bake for 30-35 minutes, or until the crumble is lightly golden and the pumpkin filling is set around the edges. The very center can have a slight wobble but should not look wet or liquid.
Transfer the pan to a wire rack and let the bars cool completely, then refrigerate for at least 1 hour before cutting for the cleanest slices.
Lift the bars from the pan using the parchment paper and cut into 9 large squares.
Notes
Use pumpkin puree, not pumpkin pie filling; canned pumpkin puree gives you control over the sweetness and spices.
Don't overbake the filling. Pumpkin custard continues setting as it cools, so remove the bars when the edges are set and the center has only a slight wobble.
Keep the crumble chunky. Larger pieces give the bars that signature crumb-bar appearance and create a better contrast against the creamy pumpkin filling.
Chill before slicing. These bars are much easier to cut cleanly once the pumpkin filling has completely cooled and chilled.