Preheat your oven to 350°F (175°C). Grease a 9×13-inch baking dish or line it with parchment paper to ensure the bars release easily once baked.
In a large bowl, mix together the all-purpose flour, old-fashioned oats, 1 cup of packed brown sugar, baking soda, and salt. Pour in the melted butter and stir until the dry ingredients are thoroughly coated and the mixture starts to clump together; this will be both the base and topping for your bars. I like to squeeze the mixture a bit with my hands to create some chunkier crumbles for extra texture.
Take about two-thirds of the crumble mixture from Step 2 and press it firmly and evenly into the prepared baking dish. This will form the base layer for your bars.
In a separate bowl, whisk together the pumpkin puree, granulated sugar, 1/4 cup brown sugar, eggs, pumpkin pie spice, and vanilla extract until everything is fully incorporated and smooth. For a little extra depth, I sometimes add a pinch more pumpkin pie spice.
Pour the pumpkin filling from Step 4 over the crumble base in the pan, spreading it evenly to cover. Sprinkle the remaining crumble mixture evenly over the top. If using, scatter the chopped walnuts across the crumble for added crunch.
Bake in the preheated oven for 40–45 minutes, or until the top is golden brown and the pumpkin filling is set. The kitchen will smell amazing as they bake!
Allow the bars to cool completely in the pan before slicing them into squares and serving. This helps the filling set and makes them easier to cut neatly.