Preheat your oven to 350°F (175°C). Line a 9x13-inch baking pan with parchment paper, leaving some overhang on the sides for easy removal later.
In a large bowl, whisk together the flour, oats, brown sugar, salt, and cinnamon until thoroughly combined. Using a pastry cutter or your fingertips, cut the cold butter into the dry ingredients until the mixture resembles coarse crumbs with some pea-sized pieces remaining.
Remove 1½ cups of the crumb mixture and stir the chopped walnuts into it. This will be your crumble topping. Set it aside in the refrigerator while you work on the remaining components.
Press the remaining crumb mixture firmly and evenly into the bottom of your prepared baking pan. Use the bottom of a measuring cup to create a smooth, compact surface. Bake for 15 minutes or until the edges just begin to turn golden.
While the crust bakes, whisk together the pumpkin puree, granulated sugar, eggs, heavy cream, and vanilla in a large bowl until smooth. Add the pumpkin pie spice, cinnamon, salt, and flour, whisking until completely incorporated.
Pour the pumpkin filling over the warm pre-baked crust, spreading it evenly with an offset spatula. Retrieve your reserved crumble-walnut mixture from the refrigerator and sprinkle it evenly over the pumpkin layer.
Bake for 40-45 minutes or until the center is just set (it should have only a slight jiggle) and the crumble topping is golden brown. A toothpick inserted into the pumpkin layer should come out mostly clean with a few moist crumbs.
Allow the bars to cool in the pan on a wire rack for 1 hour, then refrigerate for at least 2 hours before cutting.