Preheat the oven to 350°F (175°C).
In a large mixing bowl, whisk together the pumpkin puree, heavy cream, brown sugar, eggs, vanilla extract, pumpkin pie spice, and salt until smooth and well combined.
Pour the pumpkin filling into the prepared pie pan or baking dish.
In another mixing bowl, combine the rolled oats, flour, brown sugar, cinnamon, melted butter, and a pinch of salt for the crumble topping. Mix well until crumbly.
Evenly sprinkle the crumble topping over the pumpkin filling in the pie pan.
Bake in the preheated oven for about 45 minutes, or until the filling is set and the crumble is golden brown.
Remove from the oven and allow to cool slightly before serving.
Serve warm or at room temperature, optionally topped with whipped cream or vanilla ice cream for extra indulgence.